Algebra 2 Trig Honors Name_____________________________________________________ HW#4 Binomial Probability 1. If a dark-haired mother and father have a particular type of genes, they have a ¼ probability of having a light-haired baby. a. What is the probability of having a dark-haired baby?

b. If they have 3 babies, calculate P(0), P(1), P(2), and P(3), the probabilities of having exactly 0, 1, 2, and 3 dark-haired babies, respectively. c. Show that your answers to part b are reasonable by finding their sum.

2. A short multiple choice test has 4 questions. Each question has 5 choices, exactly one of which is right. Willie Makitt has not studied for the test, so he guesses at random.

a. What is the probability of guessing any one answer right? Wrong? b. Calculate his probabilities of guessing 0, 1, 2, 3, and 4 answers right. c. Perform a calculation that shows your answer to part b is reasonable. d. Willie passes the test if he gets at least 3 answers right. What is his probability of passing?

3. Three widely-separated traffic lights on U.S. 1 operate independently of each other. The probability that you will be stopped at any one of them is 40%.

a. Calculate the probability that you will make all 3 lights “green”. b. Calculate the probability that you will be stopped at exactly one, exactly two, and all three lights. c. Which is more probable, being stopped at more than one light or at one or less lights? Justify your answer.

4. Mark Wright can hit the bull’s-eye with his 22 rifle 30% of the time. He fires 5 shots a. Calculate the probability of making 0, 1, 2, 3, 4, and 5 bull’s-eyes. b. Calculate the probability that he will make at least 2 bull’s-eyes. 5. Clara Nett plays a musical solo. She is quite good, and figures that her probability of playing any one note right is 99%. The solo has 60 notes.

a. What is her probability of i. getting every note right? ii. making exactly two mistake? iii. making at least two mistakes?

iv. making more than two mistakes? b. What must be Clara’s probability of getting any one note right if she wants to have a 95% probability of getting all 60 notes right?

6. Suppose that the Dodgers and Yankees are in the World Series of baseball. From their season’s records, you predict that the Dodgers have a probability of 0.6 of beating the Yankees in any particular game. In order to win the Series, a team must win four games. a. What is the probability that the Yankees beat the Dodgers in any particular game? b. What is the probability that i. the Dodgers win all the first four games? ii. the Yankees win all the first four games?

c. For the Dodgers to win the Series in exactly 5 games, they must win exactly three of the first four games, then win the fifth game. What is the probability that the Series goes exactly 5 games, and i. the Dodgers win? ii. the Yankees win? d. What is the probability that the Series lasts i. exactly 4 games? ii. exactly 5 games? e. Recalling, as in part c, that the winner of the Series must win the last game, calculate the probability that i. the Dodgers win in 6 games. ii. the Dodgers win in 7 games. iii. the Yankees win in 6 games. iv. the Yankees win in 7 games. f. What is the most probable length of the Series, 4, 5, 6, or 7 games?