The following table shows a random sample of 100 people who go on annual vacations and the areas they prefer to go.

Vacation Area Preference

Gender

The Beach

Fishing

Mountains

Total

Female

18

16

?

45

Male

?

?

14

55

Total

?

41

?

?

Problem 1:

Complete the table.

Problem 2:

Are the events "Female" and "Beach" independent events?

Let F = Female and B = Beach.

1. P(F AND B) =
2. P(F) * P(B) =
3. Are these two numbers the same? If they are, then F and B are independent. If they are not, then F andBare not independent.

Problem 3:

Find the probability that a person is male given that the person prefers going on vacation to fish. Let M = being male and let L (for Lake) = prefers going on vacation to fish.

1. What word tells you this is a conditional?
2. Fill in the blanks and calculate the probability: P(___|___) = ___.
3. Is the sample space for this problem all 100 people surveyed? If not, what is it?

Problem 4:

Find the probability that a person is female or prefers going to the Beach.

Let F = being female and let B = going to the Beach.

1. P(F) =
2. P(B) =
3. P(F AND B) =
4. Therefore, P(F OR B) =