Trig Honors
Applications of Add/Multiply probabilities
Example 1 Flip a penny, nickel, and dime. Answer the questions that follow and record your answers in the
table.
1. Write the outcomes for flipping one time.
2. Find the probability of each event.
3. Write a mathematical calculation for each event.
Outcomes
0 tails
1 tail
2 tails
3 tails
4. Graph the probability distribution.
5. Answer the following:
a. Calculate P(Exactly two are heads)
b. Calculate P(At least two are heads)
c. Calculate P(Zero, one, two, or three heads)
d. Calculate P(Four heads)
Probability
Mathematical calculation
Example 2 If you flip a thumbtack, it can come out either “up” or “down.” Suppose that the probability of
“up” on any one flip is 0.7.
1. What is the probability of the thumbtack landing down? Explain why.
2. Predict. If you flip the thumbtack 3 times, what is more probable, getting exactly 1 thumbtack up or
getting exactly 2 thumbtacks up?
3. Write the outcomes for flipping the thumbtack three times in the table below.
4. Write a mathematical calculation in the table below to find the probability of each event.
Outcomes
Mathematical calculation of probability
0 up
1 up
2 up
3 up
5. Graph the probability distribution.
6. Answer the following:
a. Calculate P(Exactly two are down)
b. Calculate P(At least two are down)
c. Calculate P(3 down)
d. Calculate P(0, 1, 2, or 3 up)
e. Calculate P(At least one up)
f. Comparing examples 1 and 2, what are the similarities and differences?
Example 3 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 their probability of having a dark-haired baby?
b. Predict. If the parents have 3 babies, what is more probable- exactly 2 dark-haired babies or
exactly 2 light-haired babies?
c. If they have 3 babies, calculate P(0), P(1), P(2), and P(3), the probabilities of having 0,1,2,3 dark
haired babies, respectively.
d. Show that your answers to part c are reasonable by finding their sum.
e. Find P(at most 2 are dark-haired babies).
Example 4 A short multiple choice test has 4 questions. Each question has 5 choices, exactly one of which is
right. Willie Makit has not studied for the test, so he guesses at random.
a. What is his probability of guessing any one answer right? Wrong?
b. Calculate his probabilities of guessing 0,1,2,3,4 answers right.
Outcomes
Mathematical calculation of
probability
0 right
1 right
2 right
3 right
4 right
c. Perform a calculation that shows your answer to part b is reasonable.
d. Plot the graph of the probability distribution in part b.
e. Willie passes the test if he gets at least 3 answers right. What is his probability of passing?
Summary: What has been a similarity in ALL of the examples?
Homework
1. 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 probabilities that you will be stopped at exactly one, exactly two, and all three
lights.
c. Plot the graph of this probability distribution.
d. Which is more probable, being stopped at more than one light or at one or less lights? Justify
your answer.
2. Statistics show that about 5% of all males are color-blind. Suppose that 3 males are selected at random.
Let x be the number who are color-blind, and let P(x) be the probability that x of them are color-blind.
a. Calculate P(0), P(1), P(2), and P(3).
b. Plot the graph of the probability distribution.
c. What is the probability that at least 2 males are color-blind?
3. Suppose that for a certain kind of surgery, the probability that an individual will survive is 98%. If 4
people have the operation:
a. Calculate the probabilities of 0,1,2,3,4 people dying.
b. Plot the graph of the probability distribution.
c. What is the probability that at least one of the 4 people dies?
4. Tractors usually have 4 tires. Suppose that the probability of any one tire blowing out during a harvest
is 0.03.
a. What is the probability that any one tire does not blow out?
b. Calculate the probabilities of 0,1,2,3,4 tires remain intact.
c. If the farmer wants to have a 95% probability of making the trip without a blowout, what must
the reliability of each tire be? That is, what is the probability that any one tire will blow out?
5. Mark Wright can hit the bull’s eye with his 22 rifle 30% of the time. He fires 3 shots.
a. Calculate his probabilities of making 0,1,2,3 bull’s eyes.
b. Plot the graph of this probability distribution.
c. Calculate the probability that he will make at least 2 bull’s eyes.
6. Clara Nett plays a musical solo. She is quite good and figures that her probability of playing any one
note perfectly is 99%. The measure has 4 notes.
a. Calculate the probabilities of 0,1,2,3,4 notes are perfect.
b. What is the probability of playing 3 perfect measures?