Question 1. A project conducted by the Australian Federal Office of Road Safety asked people many questions about their cars. One question was the reason that a person chooses a given car, and that data is in table #4.1.4 ("Car preferences," 2013).
Table #4.1.4: Reason for Choosing a Car

Find the probability that
a.) a person chooses a car for performance.
b.) a person chooses a car for safety.

Question 2. Eyegl assomatic manufactures eyeglasses for different retailers. They test to see how many defective lenses they made in a time period. Table #4.2.2 gives the defect and the number of defects.

Table #4.2.2: Number of Defective Lenses

a.) Find the probability of picking a lens that is right shaped - small or right shaped - big.
b.) Find the probability of picking a lens that is the wrong PD or wrong axis.
c.) Find the probability of picking a lens that is not flaked.
d.) Find the probability of picking a lens that is not the wrong shape.

Question 3. In the game of roulette, there is a wheel with spaces marked 0 through 36 and a space marked 00.
a.) Find the probability of winning if you pick the number 7 and it comes up on the wheel.
b.) Find the odds against winning if you pick the number 7.
c.) The casino will pay you $25 for every dollar you bet if your number comes up. How much profit is the casino making on the bet?

Question 4. Find ₆P₃.

Question 5. How many ways can you choose three people from a group of six?

Question 6. Suppose you have an experiment where you flip a coin three times. You then count the number of tails.

Question 7. An LG Dishwasher, which costs $1000, has a 20% chance of needing to be replaced in the first 2 years of purchase. A two-year extended warranty costs $120.00 on a dishwasher. What is the expected value of the extended warranty assuming it is replaced in the first 2 years?

Question 8. Suppose a random variable, x, arises from a binomial experiment. If n = 5, and p = 0.20, find the following probabilities using technology.
a.) P(x = 1)
b.) P(x = 5)
c.) P(x ≤ 2)
d.) P(x ≥ 4)

Question 9. The proportion of brown M&M's in a milk chocolate packet is approximately 14% (Madison, 2013). Suppose a package of M&M's typically contains 52 M&M's.
a.) State the random variable.
b.) Argue that this is a binomial experiment
Find the probability that
c.) Six M&M's are brown.
d.) Twenty-five M&M's are brown.
e.) All of the M&M's are brown.
f.) Would it be unusual for a package to have only brown M&M's? If this were to happen, what would you think is the reason?

Question 10. Approximately 10% of all people are left-handed. Consider a grouping of ten people.
a.) State the random variable.
b.) Write the probability distribution.
c.) Draw a histogram.
d.) Describe the shape of the histogram.
e.) Find the mean.
f.) Find the standard deviation.