# 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**.

*G*_{1}= the event the first card drawn is gray*G*_{2}= the event the second card drawn is gray*E*= the event at least one card is gray

*P *(*G*_{1} and *G*_{2}) =

*P *(*E*) =

*P *(*G _{2}*|

*G*) =

_{1}

## Correct Answers

*P *(*G*_{1} and *G*_{2}) = 0.36

*P *(*E*) = 0.84

*P *(*G _{2}*|

*G*) = 0.6

_{1}# 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 |

- What is the probability that a randomly selected ice cream was served in a cup?
- What is the probability that a randomly selected ice cream was either chocolate or swirl?
- What is the probability that a randomly selected ice cream was chocolate served in a cup?
- What is the probability that a randomly selected ice cream was strawberry, given that it was served in a cone?
- 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 |

- 0.207965
- 0.836283
- 0.0884956
- 0.0837989
- 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.

- The nurse is a renter or lives alone. Probability =
- The nurse is a homeowner or does not live alone. Probability =
- The nurse is a renter or does not live alone. Probability =

## Correct Answers

- Probability = 1 –
^{15}⁄_{100} - Probability = 1 –
^{29}⁄_{100} - Probability = 1 –
^{21}⁄_{100}