1) Problem #PRAJBUX "PRAJBUX - 239836 - If A and B are in..." |
If A and B are independent, then... © STATS4STEM.ORG |
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2) Problem #PRAJQUV "PRAJQUV - Prob 1" |
Suppose you are drawing chips from a bag. There are 5 red chips, 6 black chips, 3 blue chips, and 4 green chips. What is the probability of drawing a red or a green chip? © STATS4STEM.ORG |
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3) Problem #PRAJQUW "PRAJQUW - Prob 2" |
You are drawing cards out from a deck of playing cards. You draw twice, replacing the cards after each draw. What is the probability of drawing a diamond suite and a queen? Round your answer to the hundredths place. © STATS4STEM.ORG |
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4) Problem #PRAJNDQ "PRAJNDQ - STATS4STEM" |
A)
A and B are independent. P(A) = 0.22 and P(B) = 0.24 Calculate P(A or B). Round answer to the nearest hundredth. © STATS4STEM.ORG |
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P(A or B) = P(A) + P(B) - P(A)*P(B) |
P(A or B) = 0.22 + 0.24 - (0.22)*(0.24) |
Therefore: P(A or B) = 0.4072 or .41 (ROUNDED) |
B)
Event G & F are independent. P(F|G) = 0.24 and P(G) = 0.35 Calculate P(F). Round answer to the nearest hundredth. |
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C)
P(D|E) = 0.6 and P(Ec) = 0.3 Calculate P(D and E) |
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P(D and E) = (0.6)*(0.7) |
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5) Problem #PRAJBU3 "PRAJBU3 - 239840 - P(A)=.8 P(B..." |
A)
P(A)=.8 P(B)=.7 P(A&B)=.6 Calculate P(B | A). Round answer to the nearest hundreths. © STATS4STEM.ORG |
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B)
Are events A and B independent? |
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C)
Calculate P(A | B). Round to the nearest hundreths. |
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6) Problem #PRAJBT2 "PRAJBT2 - 239808 - X and Y are disjo..." |
X and Y are disjoint/mutually exclusive events. If P(X) = 0.15 and P(X or Y) = 0.47, find P(YC). Round answer to the nearest hundredth. © STATS4STEM.ORG |
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P(X or Y) = 0.15 + P(Y) = 0.47 |
P(Y) = 0.32 |
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7) Problem #PRAJBTZ "PRAJBTZ - 239807 - The probability t..." |
The probability that Jane will get a cheeseburger and French fries is 0.7. The probability that she will get a cheeseburger is 0.95. What is the probability that she will get French fries given that she gets a cheeseburger? Round answer to the nearest hundredth. © STATS4STEM.ORG |
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8) Problem #PRAJKWU "PRAJKWU - 247583 - The length of a h..." |
A)
The length of a hockey stick is normally distributed with a mean of 42 inches and a standard deviation of 3 inches. a.) Calculate P(X < 41). Round answer to the nearest hundredth. Click here for a link to a z-table. © STATS4STEM.ORG |
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z = (x-μ)/σ |
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B)
b.) Calculate P(X > 46). Round to the nearest hundredth. |
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z = (x-μ)/σ |
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P(X < 46) = 0.9082 Therefore, the P(X > 46) = 1 - P(X < 46) = 1 - 0.9082 ** Hint: Remember to subtract from 1 when the problem is a ">" problem ** |
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C)
c). Calculate P(X < 41 or X > 46). Round to the nearest hundredth. |
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When calculating "or" problems, add the probabilities together: i.e. P(X < 41) + P(X > 46) |
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P(X < 41 or X > 46)= P(x < 41) + P(x > 46) = 0.37 + 0.09
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9) Problem #PRAEFVW "PRAEFVW - Probability - Addition and multiplication rules - OLI" |
Below is the probability distribution for blood types:
Three people are chosen at random. What is the probability that they all have the same blood type? Round answer to the nearest hundredths. © STATS4STEM.ORG |
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P( (O and O and O) OR (A and A and A) OR (B and B and B) OR (AB and AB and AB) ) |
.443 + .423 + .103 + .043 |
Answer = 0.16 (Rounded)
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10) Problem #PRAJBT4 "PRAJBT4 - 239810 - If the probabilit..." |
If the probability of A = 68%, what is the probability of Ac? Round answer to the nearest hundredth. © STATS4STEM.ORG |
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11) Problem #PRAJBUS "PRAJBUS - 239831 - If P(A) = .27, P(..." |
If P(A) = .27, P(B) = .67, and P(A and B) = .59, what does P(A or B) equal? Round answer to the nearest hundredth. © STATS4STEM.ORG |
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12) Problem #PRAJBUZ "PRAJBUZ - Baseball" |
In order for a baseball to pass inspection it must weigh 5 ounces. There is a 2% chance that any one ball fails inspection. If 127 balls were sent for inspection, what is the probability that at least 1 will fail inspection? Round answer to the nearest hundredths. © STATS4STEM.ORG |
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13) Problem #PRAJBUD "PRAJBUD - 239819 - If P(A) and P(B) ..." |
A)
If P(A) and P(B) are independent then if P(A)=.32 P(A&B)=.08 The P(B)=? © STATS4STEM.ORG |
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OR P(A)*P(B) = P(A&B) |
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B)
If A & B are independent and P(A) = 0.2 and P(B) = 0.9, calculate P(A&B). |
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C)
If P(A) and P(B) are disjoint/mutually exclusive and: P(A)=.27 P(B)=.39 Calculate P(A&B). Round to nearest hundreth |
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14) Problem #PRAJVCD "PRAJVCD - 255691 - Eat-A-Donut offer..." |
A)
Eat-A-Donut offers the following donut selection: People pay by the gram. The distribution of individual donut weights (in grams) is found below: Powdered ~ N(25, 1) Boston Cream ~ N(29, 1.3) Almond ~ N(26, 1.1) Jelly ~ N(28, 1.2) Vegan ~ N(26.5, 0.8) Glazed ~ N(24, 0.7) A customer walks in and asks for a random donut from the 6 listed above. What is the probability that the randomly chosen donut is a Powdered donut that weighs less than 25 grams? Assume that each of the six donuts has an equally likely chance of being chosen. Round answer to the nearest hundredth. © STATS4STEM.ORG |
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P(Powdered Donut and Powdered Donut weighs less than 25 grams) = (1/6) * (1/2) = 1/12 = 0.08 (ROUNDED) |
B)
A customer orders a random selection of a dozen donuts from the 6 donuts listed above. What is the probability that none of them are Glazed? Assume that each of the six donuts has an equally likely chance of being chosen. Round answer to the nearest hundredth. Note: A dozen = 12 |
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C)
You go to Eat-A-Donut and pick up a dozen randomly chosen donuts. As you are heading back to your mom's house, you remember that your mom loves Jelly. Calculate the probability that you have at least 1 jelly donut for your mom. Round answer to the nearest hundredth. |
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15) Problem #PRAJBT8 "PRAJBT8 - 239814 - Orange Red Gre..." |
A)
Refer to the above table displaying the probability of choosing a given color out of a bag of Skittles. Round answers to the nearest hundredth. A.) What is the probability of getting a yellow Skittle? Round answer to the nearest hundredth. © STATS4STEM.ORG |
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B)
B.) What is the probability of NOT getting an orange Skittle? Round answer to the nearest hundredth. |
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C.) What is the probability of getting a red or green Skittle? Round answer to the nearest hundredth. |
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D)
D.) You pick two Skittles from the bag. What is the probability that you select a red and a green Skittle? Assume independence. Round answer to the nearest hundredth. |
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16) Problem #PRAJBTV "PRAJBTV - 239803 - Events A and B ar..." |
Events A and B are mutually exclusive/disjoint. The probability of Event A occurring is 0.37 and the probability of Event B occurring is 0.49. What is P(A and B)? Round answer to the nearest hundredth. © STATS4STEM.ORG |
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17) Problem #PRAJBSV "PRAJBSV - 239772 - Grandma Heiser&rs..." |
A)
Grandma Heiser’s cookie factory makes four types of cookies: oatmeal, gingerbread, chocolate chip, and sugar. The distribution of cookie type of an assorted cookie holiday tin:
What is the probability of getting sugar cookies in this tin? Round answer to the nearest hundredth. © STATS4STEM.ORG |
Exact Match (case sensitive):
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B)
If you close your eyes and choose two cookies, what is the probability that you get one oatmeal cookie and one sugar cookie? Round to the nearest hundredth. |
Exact Match (case sensitive):
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18) Problem #PRAJBTT "PRAJBTT - 239801 - Use this table to..." |
A)
Use this table to answer the following questions.
© STATS4STEM.ORG |
Check All That Apply:
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B)
Given that he is a male, what is the probability that a randomly chosen subject does not own a dog? Round to the nearest hundredth. |
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C)
What is the probability that a randomly chosen subject does not have a dog? Round to the nearest hundredth. |
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19) Problem #PRAJBTA "PRAJBTA - 239785 - The probability t..." |
The probability that a randomly chosen person has a dog is 0.34. The probability that a randomly chosen person will have a dog and be walking in the park is 0.03. The probability that a randomly chosen person is walking in the park or has a dog is 0.40. What is the probability that a randomly chosen person is not walking in the park? Round to the nearest hundredths. © STATS4STEM.ORG |
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20) Problem #PRAJBTC "PRAJBTC - 239787 - Here are the coun..." |
A)
Here are the counts of students in a class, classified by gender and hair color:
Round all answers to the nearest hundredth. a) What is the probability that a student chosen at random has blonde hair? © STATS4STEM.ORG |
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B)
b) What is the probability that you choose a male, given that they have black hair? |
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c) What is the probability that you choose a person with brown hair, given that they are female? |
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21) Problem #PRAEGC6 "PRAEGC6 - Probability - Card Deck - EJS" |
A)
You randomly pick a card from a deck of cards containging 52 cards (see above). What is the probability, as a percentage, that you pick a random card and it is a 10 or Queen? Answer should be a percentage rounded to the nearest whole number. Do not include % sign. |
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B)
You randomly pick a card from a deck of cards containging 52 cards (see above). What is the probability, as a percentage, that you pick a random card and it is a Heart or Queen? Answer should be a percentage rounded to the nearest whole number. Do not include % sign. |
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22) Problem #PRAEGGU "PRAEGGU - Probability - Conditional - IL ElemS" |
The World Wide Insurance Company found that 53% of the residents of a city had homeowner's insurance with the company. Of these clients, 27% also had auto insurance with the company. If a resident is selected at random, find the probability (as a percentage) that the resident has both homeowner's and auto insurance with the World Wide Insurance Company. Round answer to the nearest hundredth. |
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23) Problem #PRAJBUE "PRAJBUE - 239820 - A deck of cards: ..." |
A)
A deck of cards: What is the probability of drawing 2 of the same suit in a row from a regular deck of cards (without replacement)? © STATS4STEM.ORG |
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B)
What is the probability of drawing 2 of the same suit in a row from a regular deck of cards (with replacement)? |
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24) Problem #PRAJBTW "PRAJBTW - 239804 - A class is asked ..." |
A class is asked about their pets. The probability that a randomly selected student has a cat given that they have a dog is 0.4. The probability that the same randomly selected student has a cat is 0.3. Are the probabilities of a student having a cat and a dog independent? © STATS4STEM.ORG |
Multiple Choice:
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P(having a cat) = 0.3 |
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25) Problem #PRAEH2M "PRAEH2M - Probability - General Addition Rule - EJS" |
The probability that a wizard owns a broom is 0.75, that a wizard owns a wand is 0.35, and that a wizard owns both a broom and a wand is 0.20. Calculate the probability that a wizard owns either a broom or wand. Round answer to the nearest hundredth. © STATS4STEM.ORG |
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26) Problem #PRAJ8HU "PRAJ8HU - STATS4STEM" |
A)
A and B are independent. P(A) = 0.37 and P(B) = 0.42 Calculate P(A or B). Round answer to the nearest hundredth. © STATS4STEM.ORG |
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P(A or B) = P(A) + P(B) - P(A)*P(B) |
P(A or B) = 0.37 + 0.42 - (0.37)*(0.42) |
Therefore: P(A or B) = 0.6346 or .63 (ROUNDED) |
B)
P(D|E) = 0.57 and P(Ec) = 0.37 Calculate P(D and E) |
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P(D and E) = (0.57)*(0.63) |
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C)
Event G & F are independent. P(F|G) = 0.17 and P(G) = 0.25 Calculate P(F). Round answer to the nearest hundredth. |
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27) Problem #PRAKEHQ "PRAKEHQ - STATS4STEM" |
A)
A and B are independent. P(A) = 0.34 and P(B) = 0.17 Calculate P(A or B). Round answer to the nearest hundredth. © STATS4STEM.ORG |
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P(A or B) = P(A) + P(B) - P(A)*P(B) |
P(A or B) = 0.34 + 0.17 - (0.34)*(0.17) |
Therefore: P(A or B) = 0.4522 or .45 (ROUNDED) |
B)
Event G & F are independent. P(F|G) = 0.17 and P(G) = 0.39 Calculate P(F). Round answer to the nearest hundredth. |
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C)
P(D|E) = 0.9 and P(Ec) = 0.4 Calculate P(D and E) |
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P(D and E) = (0.9)*(0.6) |
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28) Problem #PRAKEKB "PRAKEKB - 272243 - Bagel Heaven offe..." |
A)
Bagel Heaven offers the following bagel selection: People pay by the gram. The distribution of individual bagel weights (in grams) is found below: Blueberry ~ N(35, 2) Garlic ~ N(39, 2.3) Everything ~ N(36, 2.1) Raisin ~ N(38, 2.2) Plain ~ N(36.5, 1.8) Poppy Seed ~ N(34, 1.7) A customer walks in and asks for a random bagel from the 6 listed above. What is the probability that the randomly chosen bagel is a Blueberry bagel that weighs less than 35 grams? Assume that each of the six bagels has an equally likely chance of being chosen. Round answer to the nearest hundredth. © STATS4STEM.ORG |
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P(Blueberry bagel and blueberry bagel weighs less than 35 grams) = (1/6) * (1/2) = 1/12 = 0.08 (ROUNDED) |
B)
A customer orders a random selection of a baker's dozen of bagels (13 bagels) from the 6 bagels listed above. What is the probability that none of them are Poppy Seed? Assume that each of the six bagels has an equally likely chance of being chosen. Round answer to the nearest hundredth. |
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C)
You go to Bagel Heaven and pick up a baker's dozen of randomly chosen bagels. As you are heading back to your mom's house, you remember that your mom loves Raisin. Calculate the probability that you have at least 1 Raisin bagel for your mom. Round answer to the nearest hundredth. |
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29) Problem #PRAKEKE "PRAKEKE - 272246 - The probability t..." |
The probability that Taryn will get a frappe and a hot dog From Sullies is 0.3. The probability that she will get a frappe is 0.81. What is the probability that she will get a hot dog given that she gets a frappe? Round answer to the nearest hundredth. © STATS4STEM.ORG |
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30) Problem #PRAKEKF "PRAKEKF - 272247 - Here are the coun..." |
A)
Here are the counts of blocks in a box, classified by shape and color:
a) What is the probability that a block chosen at random is yellow? © STATS4STEM.ORG |
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b) What is the probability that you choose a red block, given that it is a square? |
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c) What is the probability that you choose a square block, given that it is blue? |
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31) Problem #PRAKFTQ "PRAKFTQ - 273433 - An study was cond..." |
A)
A study was conducted using traffic data. The study found that the probability that a driver goes through a red light to be 0.10. Further analysis found that the probability of a car accident given that a driver goes through a red light to be 0.7, while the probability that a driver gets into an accident given that they don't go through a red light to be 0.10. Note on notation: "R" represents a car going through a red light while "A" represents a car getting into an accident. All underlined letters represent probabilities. Click here if you can't see the image. STRONG SUGGESTION: THIS PROBLEM HAS 11 QUESTIONS AND IT IS HIGHLY RECOMMENDED THAT YOU RECREATE THE ABOVE TREE DIAGRAM AND FILL IN THE LETTERS B THROUGH G. THIS WILL GREATLY IMPROVE YOUR UNDERSTANDING OF THE PROBLEM WHILE MAKING THE PROBLEM GO BY FASTER. Refer to the tree diagram found above, all underlined letters represent probabilities, what is the value of B? Round answer to the nearest hundredth. © STATS4STEM.ORG |
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B)
Refer to the tree diagram found above, what is the value of C? Round answer to the nearest hundredth. |
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C)
Refer to the tree diagram found above, D represents: |
Multiple Choice:
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D)
Refer to the tree diagram found above, what is the value of D? Round answer to the nearest hundredth. |
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E)
What is the value of P(Ac|Rc)? Round answer to the nearest hundredth. Link to the tree diagram. |
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F)
What is the probability a random car goes through a red light and gets into an accident? Link to tree diagram. |
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G)
What is the probability a random car doesn't go through a red light and gets into an accident? Round answer to the nearest hundredth. Link to tree diagram. |
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H)
What is the probability a random car gets into an accident? Round answer to the nearest hundredth. Link to tree diagram. |
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I)
What is the probability that a car that was in an accident drove through a red light? Round answer to the nearest hundredth. Link to tree diagram. |
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J)
What is the probability a random car doesn't get into an accident? Round answer to the nearest hundredth. Link to tree diagram. |
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K)
Given that a car did not get into an accident, what is the probability that it went through a red light? Round answer to the nearest hundredth. Link to tree diagram. |
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32) Problem #PRAJBYM "PRAJBYM - 239950 - In what scenario ..." |
In what scenario can P(B|A)= P(B)? © STATS4STEM.ORG |
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33) Problem #PRAEH2N "PRAEH2N - Probability - Tree Diagram - Conditional Probability - EJS" |
You are presented with three urns. Each urn has 10 marbles. In addition, each urn holds only black or red marbles. Urn 1 has 3 red marbles. Urn 2 has 8 red marbles. Urn 3 has 5 red marbles. You randomly pick 1 marble from 1 of the three urns. Calculate the probability that it is a black marble. Round answer to the nearest hundredth. © STATS4STEM.ORG |
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As you see above, the probabilities all add up to 1. Thus each outcome, with corresponding probability in our sample space, is accounted for. |
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34) Problem #PRAKEVH "PRAKEVH - 272528 - Here are the coun..." |
A)
Here are the counts of employees in an office, classified by gender and eye color:
Round all answers to the nearest hundredth. a) What is the probability that an employee chosen at random has hazel eyes? Round answer to the nearest hundredth. © STATS4STEM.ORG |
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b) What is the probability that you choose a male, given that they have green eyes? Round answer to the nearest hundredth. |
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c) What is the probability that you choose a person with brown eyes, given that they are female? Round answer to the nearest hundredth. |
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d) What is the probability that you choose a female with green eyes? Round answer to the nearest hundredth. |
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e) What is the probability that you choose a male with brown eyes? Round answer to the nearest hundredth. |
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35) Problem #PRAP6K5 "PRAP6K5 - Problem #383744" |
Each of two events have probabilities greater than 0. Which of the following statements is correct for the two events? |
Multiple Choice:
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