3 Probability

Problem 1

Suppose that you have 12 cards. 7 are gray and 5 are yellow. The 7 gray cards are numbered 1, 2, 3, 4, 5, 6, and 7. The 5 yellow cards are numbered 1, 2, 3, 4, and 5. The cards are well shuffled. You randomly draw one card.

  • G = the event the card drawn is gray
  • E = the event the card drawn is even-numbered

P (G) =

P (E) =

P (G and E) =

P (G or E) =

P (G|E) =

P (E|G) =

 

Correct Answers

P (G) = 0.583333

P (E) = 0.416667

P (G and E) = .25

P (G or E) = .75

P (G|E) = .6

P (E|G) = .428571

Problem 2

Suppose that you have 15 cards. 9 are gray and 6 are yellow. The cards are well shuffled. You randomly draw two cards, with replacement.

  • G1 = the event the first card drawn is gray
  • G2 = the event the second card drawn is gray
  • E = the event at least one card is gray

 

P (G1 and G2) =

P (E) =

P (G2|G1) =

 

Correct Answers

P (G1 and G2) = 0.36

P (E) = 0.84

P (G2|G1) = 0.6

Problem 3

In a box of assorted cookies, 43% contain chocolate, 12% contain nuts, and 3% contain both chocolate and nuts. Jada is allergic to both chocolate and nuts.

What is the probability that a cookie contains chocolate or nuts (they can’t eat it)?

What is the probability that a cookie does not contain chocolate or nuts (they can eat it)?

 

Correct Answers
  • 52%
  • 48%

Problem 4

A soft-serve ice cream shop sold 226 ice creams in a day. The following table identifies the ice creams they sold by flavor and whether they were served in a cup or cone. Fill in the missing values.

Flavor Chocolate Vanilla Swirl Strawberry Total
Cup 20 No Data 17 4 47
Cone 82 12 No Data 15 No Data
Total No Data 18 No Data No Data No Data
  1. What is the probability that a randomly selected ice cream was served in a cup?
  2. What is the probability that a randomly selected ice cream was either chocolate or swirl?
  3. What is the probability that a randomly selected ice cream was chocolate served in a cup?
  4. What is the probability that a randomly selected ice cream was strawberry, given that it was served in a cone?
  5. What is the probability that a randomly selected ice cream was not chocolate?

 

Correct Answers
Flavor Chocolate Vanilla Swirl Strawberry Total
Cup 20 6 17 4 47
Cone 82 12 70 15 179
Total 102 18 87 19 226
  1. 0.207965
  2. 0.836283
  3. 0.0884956
  4. 0.0837989
  5. 0.548673

 

Problem 5

One hundred nurses were surveyed about their living situation. The results of this survey are given in the following table.

No Data Renter ([latex]R[/latex]) Homeowner ([latex]R^{\prime}[/latex]) Total
Lives alone ([latex]A[/latex]) 29 21 50
Does not live alone ([latex]A^{\prime}[/latex]) 35 15 50
Total 64 36 100

If a nurse is selected at random from those surveyed, find the probability of each of the following events.

 

  1. The nurse is a renter or lives alone. Probability =
  2. The nurse is a homeowner or does not live alone. Probability =
  3. The nurse is a renter or does not live alone. Probability =

 

Correct Answers
  1. Probability = 1 – 15⁄100
  2. Probability = 1 – 29⁄100
  3. Probability = 1 – 21⁄100

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Statistical Problem Sets in WeBWorK Copyright © 2023 by Rachael Norton and Peter Staab is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.

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