1. The following data were gathered for 110workers. Of those workers,44were women,2women earned more than $40,000, and 48men earned $40,000 or less.

(a) Find the probability that an individual is a woman earning $40,000 or less.

2. If two fair dice are rolled, find the probability that the sum of the dice is 9, given that the sum is greater than 6.

3. Two cards are drawn without replacement from an ordinary deck, find the probability that the second is not a diamond, given that the first is not a diamond.

4.Two cards are drawn without replacement from an ordinary deck. Find the probability that two face cards are drawn.

5.A bicycle factory runs two assembly lines, A and B. 94% of line A's products pass inspection and 87% of line B's products pass inspection. 40% of the factory's bikes come off assembly line B and the rest come off line A.

Find the probability that one of the factory's bikes passed inspection and came off assembly line Upper B.

6.According to a recent report, 66.4% of men and 50.8% of women in the United States were overweight. Given that 48.4% of Americans are men and 51.6% are women, find the probability that a randomly selected American fits the following description.

(a) An overweight man

(b) Overweight

(c) Are the events that an adult is a man and that an adult is overweight independent? Explain.

7.Suppose 22% of the population are 62 or over, 26% of those 62 or over have loans, and 59% of those under 62 have loans. Find the probabilities that a person fits into the following categories.

(a) 62 or over and has a loan

(b) Has a loan

(c) Are the events that a person is 62 or over and that the person has a loan independent? Explain.

8.The Motor Vehicle Department has found that the probability of a person passing the test for a driver's license on the first try is 0.77. The probability that an individual who fails on the first test will pass on the second try is 0.83, and the probability that an individual who fails the first and second tests will pass the third time is 0.71.

Find the probabilities that an individual will do the following.

a. P(Fail both the first and second tests)

b. P(Fail three times in a row)

c. P(Require at least two tries)