Binomial Probability - Weebly



AP Statistics: Binomial Probability Practice Date_______________________

An experiment is binomial if

1) The experiment has n identical trials

2) Each trial results in one of two outcomes

3) The trials are independent

4) There is a fixed number n of observations.

Tell whether each of the following is a binomial experiment:

1) Flipping a coin 5 times and counting the number of heads

2) Drawing 5 cards, without replacement, from a deck and counting the aces

3) Rolling a die 5 times and counting the face values

4) Shooting 5 foul shots in basketball and counting the baskets made

5) Rolling a die 5 times and counting the number of 2’s

The probability of k successes in n trials where the probability of success is p:

P(x = k) = [pic]

Example 1: Suppose a coin is bent so that the probability of it coming up “heads” on any toss is .4. If the coin is tossed 3 times, find the probability of getting exactly 2 “heads.”

Example 2: The probability that an individual is right handed is .95. Find the probability that at least one of 10 randomly chosen students is left handed.

Example 3: A basketball player’s free-throw percentage is .75. What is the probability that the player makes at least 4 baskets in his next 5 free throws?

Example 4: A quiz has multiple choice questions, each with 4 choices. If you guess at every question, what is the probability of getting at least 5 of 8 questions correct?

Express each of the following in a form that can be used with binomialcdf:

1. P (x < 5)

2. P(x > 5)

3. P(x > 5)

4. P(2 < x < 15)

5. P(3 < x < 15)

Binomial Probability Distribution

Let X = the number of “successes” in a binomial experiment with n trials, where p is the probability of success. P(X = r) = n C r (p)r (1 – p)n – r

On the calculator: binompdf (n, p, r) = P(X = r) binomcdf (n, p, r) = P(X ≤ r)

1. About 85% of students at a local high school favor school-sponsored extracurricular activities. If 20 randomly selected students are asked whether they support school-sponsored extracurricular activities, what is the probability that 19 will say “yes?”

2. A multiple choice exam has 8 questions. Each question has 4 choices. Assuming the answers are random guesses, what is the probability of getting at least 5 answers correct?

3. 28% of the students in grades 3-12 say that, other than their parents and teachers, Star Trek programs most strongly influence their interest in science. If 18 randomly selected students in grades 3-12 are asked whether Star Trek programs most influence their interest in science (yes or no), find the probability that 4 students say “yes.”

4. A recent survey of randomly selected adults found that 66% should rather have more money than more time. What is the probability that 8 or fewer out of 10 randomly selected adults would rather have more money than time?

5. Suppose 30% of all people eat dessert in the kitchen. If 8 randomly selected people are polled, what is the probability that less than 3 of them eat dessert in the kitchen?

6. In the United States, 57% of cat owners and 32% of dog owners say their pet usually sleeps on the bed with them. Out of 20 randomly selected cat owners, what is the probability that 15 will say their cat usually sleeps on the bed with them?

7. Approximately 42% of all computers are located in private homes. Out of 20 randomly selected computers, what is the probability that half of them are located in private homes?

8. In a cooking class, 1 out of 5 soufflés that Sabrina makes will collapse. She is preparing 6 soufflés to serve at a party. What is the probability that more than 4 of them do not collapse?

9. A die is tossed 5 times. What is the probability of getting no more than two 4’s?

10. Marie guesses on all 10 true/false questions on her psychology test. Find the probability that she gets at least 6 correct answers.

11. A yellow bellied sapsucker has a .58 probability of surviving adulthood. Given a nest of six eggs, what is the probability that at least 5 will survive.

12. In baseball, the World Series matches the champion from the American League against the champion from the National League in a best of 7 series games (meaning the first team to win 4 games is the World Series champion). If the two teams are evenly matched, what is the probability that the World Series will end in exactly 5 games?

Answers: 1: .1368 2: .0273 3: .1892 4: .9035 5: .5518 6: .0496 7: .1359

8: .6554 9: .9645 10: .3770 11: .2035 12: .25

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