# Given probabilities

8. Joe is considering one of three locations for his business. There is a 45% probability he will choose location A, a 25% probability he will choose B and a 30% probability he will choose location C. If he chooses A the probability that he will make a profit in the first six months is 55%, if he chooses B the probability of making a profit in the first six months is 50% and if he chooses C the probability of making a profit in the first six months is 35%.

Determine the following probabilities to three decimal places.

a). What is the probability that Joe will choose location A and make a profit in the first six months? P(Location A and makes a profit)

______ _____________

b) What is the probability that Joe will choose location C and does NOT make a profit in the first six months? P(Location C and does not make a profit)

_____________________

b). What is the probability Joe will make a profit in the first six months?

________________________________

9. ABC home builders sold 50 new homes last year. Of the homes, 20 have skylights; 25 have attached garages; and 5 have both a skylight and an attached garage. Others have neither garages nor skylights.

Determine the following probabilities to three decimal places.

Find the probability that a randomly selected house will:

a). Have both a skylight and an attached garage:

b). Have a skylight only:

c). Have either a skylight or an attached garage (or both):

d). Have a skylight given that we know it has an attached garage:

e). Have an attached garage given that we know it has a skylight:

10. The executives at a text book publishing company wants to gather data from universities on statistics text books currently in use. Identify the correct sampling method being used in each of the following scenarios:

a.) Using a list of all universities in the United States, they randomly choose a number between 1 and 35 to be the first university questioned. Then they question every 17thth university after the first one.

__ ________________

b.) They list all of the universities in the United States. Then 100 random numbers are generated and the universities that correspond with the random numbers are chosen.

__ ________________

c.) They randomly select 25 states from all states in the United States and question every university in each of the 25 states.

___ _______________

d.) They randomly select 30 universities from each state in the United States and question these selected universities.

___ _______________

11. A group of 300 heads of households was surveyed to determine if their marital status was related to home ownership. Complete the table to answer the questions below:

Marital Status

Living

Status Single (never married)

Divorced

Married Totals

Own home 33 39 83

Rent 15 18 52

Live with family 32 13 15

Totals 300

Determine each probability: (Round answers to three decimal places) (1 pt ea)

a). What is the probability that a randomly selected head of household will rent?

b). What is the probability that a randomly selected head of household will be single?

c). What is the probability that a randomly selected head of household will own a home and be married?

d). What is the probability that a randomly selected head of household is single given he/she lives with a family?

e). What is the probability that a randomly selected head of household will rent given he/she is divorced?

f). What is the probability that a randomly selected head of household will rent given he/she is married?

g). Are marital status and living situation independent or dependent?

h). Explain your answer in part g using probabilities:

_______________________________________________________

12. Given the following probability distribution, determine the given probabilities:

x P(x)

0 0.10

1 0.20

2 0.55

3 0.15

a). P(x < 1) = b). P(1 < x < 3) =

c). P(x > 2) = d). P(1 < x < 3) =

e). Expected value of x = f). Standard deviation =

13. A study shows that 20% of cars in the state of Ohio have improperly functioning emission control systems. If a random sample of 15 cars is taken, determine the following: (Round answers to three decimal places)

a). What type of probability distribution does this describe and why?__ ______

________________________________________________________________

b). The probability that exactly 2 will be improperly functioning:

c). The probability that no more than 2 will be improperly functioning:

d). The probability that at least 2 are improperly functioning:

e). The expected number of cars with improperly functioning systems out of the sample of 15:

f). The standard deviation of the probability distribution:

14. Suppose 10-mile race times have an average runnerâ??s finish time of 80 minutes with a standard deviation of 7 minutes. There is strong reason to believe the times are NOT normally distributed.

a). If 750 people run, at least how many people will have finish times within 2 standard deviations of the mean? _______________

b). If you were one of these people, in what time interval would you have run the race?

_______________________

#### Solution Summary

Given probabilities are featured.