Probability Models and Rules Homework

Name ______Period ______

Special Topics – Section 8.1

Probability Models and Rules Homework

1. Probability is a measure of how likely an event is to occur. Match one of the probabilities that follow with each statement about an event. (The probability is usually a much more exact measure of likelihood than is the verbal statement.)

0, 0.01, 0.3, 0.6, 0.99, 1

1.  This event is impossible. It can never occur.

2.  This event is certain. It will occur on every trial of the random phenomenon.

3.  This event is very unlikely, but it will occur once in a while in a long sequence of trials.

4.  This event will occur more often than not.

2. Of voters in a recent election, 57% were male, 64% were Democrat, and 35% were both male and Democrat.

a) What is the probability that a voter chosen at random is female?

b) What is the probability that a voter chosen at random is Republican?

c) Is being male or Democrat independent of each other?

3. You read in a book on poker that the probability of being dealt three of a kind in a five-card poker hand is 1/50. What does this mean?

a) If you deal thousands of poker hands, the fraction of them that contain three of a kind will be very close to 1/50.

b) If you deal 50 poker hands, exactly one of them will contain three of a kind.

c) If you deal 10,000 poker hands, exactly 200 of them will contain three of a kind.

4. If two coins are flipped and then a die is rolled, the sample space would have _____ different

outcomes.

Exercises 5 to 9 use this probability model for the blood type of a randomly chosen person in the United States:

5. If this model represents all of the blood types a person could have, what it is the probability of selecting a person having type AB blood?

6. If a person is chosen randomly, what is the probability of choosing a person with either Type O or Type B?

7. If a person is chosen randomly, what is the probability of choosing a person who does not have Type AB?

8. If a person is chosen randomly, what is the probability of choosing a person who does not have either Type A or Type B?

9. Maria has type A blood. She can safely receive blood transfusions from people with blood types O and A. What is the probability that a randomly chosen American can donate blood to Maria?

10. If you flip 3 coins, how many possible outcomes are there? Write out the sample space for this scenario. If you flip 4 coins, how many outcomes are there?

11. Describe the sample space for each of the following using the notation you learned in class. It is possible and easier to use words instead of numbers in crafting your answer.

a) Choose a student in your class at random. Ask how much time (in hours) that student has spent studying during the past 24 hours.

b) The Physicians’ Health Study asked 11,000 physicians to take an aspirin every other day and observed how many of them had a heart attack in a five-year period.

c) In a test of a new package design, you drop a carton of eggs from a height of 1 foot and count the number of broken eggs.

d) Choose a student in your class at random. Ask how much cash that student is carrying.

e) A nutrition researcher feeds a new diet to a young male white rat. The response variable is the weight (in grams) that the rat gains in 8 weeks.

12. Many email messages are “spam.” Choose a spam email message at random. Here is the probability model for the topic of a randomly chosen spam email message:

1.  What is the probability that a spam email does not concern one of these topics?

2.  Corinne is particularly annoyed by spam offering “adult” content and scams. What is the probability that a randomly chosen spam email falls into one of these categories?

13. Some situations refer not to probabilities, but to odds. The odds against an event E are equal to P(EC)/P(E). If there are 3:2 odds against a particular horse winning a race, what is the probability that the horse wins?

14. The Punnett square is a diagram biologists use to determine the probability of offspring having certain genetic makeup. Suppose “B” represents the gene for brown eyes and “b” represents the gene for blue eyes. In genetics, capital letters refer to dominant traits, so a person receiving both “B” and “b” generally has brown eyes. This diagram shows the possibilities for the child of two Bb parents. Each parent gives the child one of its 2 genes with equal probability. What is the probability that this child will receive the genetic makeup for brown eyes?

15. Suppose you select a card from a standard deck of 52 cards. Determine the probabilities for selecting:

a) a red card.

b) a heart.

c) a queen and a heart.

d) a queen or a heart.

e) a queen that is not a heart.

16. If a man has 4 pairs of pants, 5 shirts, 3 ties, and 2 pairs of shoes, how many different outfits can this man put on?