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. Eyeglassomatic 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

Find the probability of picking a lens that is right shaped - small or right shaped - big.
Find the probability of picking a lens that is the wrong PD or wrong axis.
Find the probability of picking a lens that is not flaked.
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.
Find the probability of winning if you pick the number 7 and it comes up on the wheel.
Find the odds against winning if you pick the number 7.
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.
State the random variable.
Write the probability distribution for the number of tails.
Find the mean number of tails.
Find the standard deviation for the number of tails.
Find the probability of having one or more 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.
State the random variable.
Argue that this is a binomial experiment
Find the probability that
Six M&M's are brown.
Twenty-five M&M's are brown.
All of the M&M's are brown.
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.
State the random variable.
Write the probability distribution.
Draw a histogram.
Describe the shape of the histogram.
Find the mean.
Find the standard deviation.