Question

The effectiveness of birth control is measured by comparing what percentage of women of childbearing age become pregnant in a year, while using the method. The table below gives the data from a clinical trial for a new birth control pill.

	Becomes Pregnant within one year	Does not become pregnant within one year	Total
Uses birth control pill	26	275	301
No contraceptive method	113	22	135
Total	139	297	436

a. Given that a woman uses birth control, find the conditional probability that she becomes pregnant within one year. Round your answer to 4 decimal places.

b. Given that a woman does not use birth control, find the conditional probability that she becomes pregnant within one year. Round your answer to 4 decimal places.

c. Are the events "a randomly selected woman uses birth control" and "a randomly selected woman becomes pregnant within one year" independent? Why or why not?

Select your answer from one of the following options.

• a.No. A woman can still become pregnant while on birth control.
• b.No. Using birth control significantly decreases the probability that a woman will become pregnant within one year.
• c.Yes. A woman can still become pregnant while on birth control.
• d.Yes. Using birth control significantly decreases the probability that a woman will become pregnant within one year.

d. Are the events "a randomly selected woman uses birth control" and "a randomly selected woman becomes pregnant within one year" mutually exclusive? Why or why not?

Select your answer from one of the following options.

• a.No. A woman can still become pregnant while on birth control.
• b.No. Using birth control significantly decreases the probability that a woman will become pregnant within one year.
• c.Yes. A woman can still become pregnant while on birth control.
• d.Yes. Using birth control significantly decreases the probability that a woman will become pregnant within one year.

Answer 1