Algebra 2 Trig Honors
HW#3 Binomial Probability
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Please show all of your work in space below each problem number
1. If a dark-haired mother and father have a particular type of gene, they have a ¼ probability of having a lighthaired 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?
Taken from Algebra and Trigonometry Functions and Applications by Paul A. Foerster