Question

A women-only gym has 60% of its members married. 75% of the married women exercise in the morning and 30% of the single women exercise in the morning. Are being married and exercising in the morning independent?

A) Yes. P(married | exercise in the morning) = P(exercise in the morning | married) = 75%
B) Yes. P(married and exercise in the morning) = P(married)·P(exercise in the morning) = 45%
C) No. P(married and exercise in the morning) = 60% & P(married)·P(exercise in the morning) = 42%
D) No. P(married and exercise in the morning) = 45% & P(married)·P(exercise in the morning) = 34.2%

Answer 1

D) No. P(married and exercise in the morning) = 45% & P(married)·P(exercise in the morning) = 34.2%

Explanation:

Answer 2

Given:
Women only gym:
60% married women
75% of the married women exercise in the morning
30% of the single women exercise in the morning

60% married women + 40% single women = total women members

60% married
75% exercise in the morning
25% exercise in the afternoon or evening

40% single
30% exercise in the morning
70% exercise in the afternoon or evening

Exercise in the morning
married: 60% x 75% = 45%
single: 40% x 30% = 12%

B) Yes. P(married and exercise in the morning) = P(married)·P(exercise in the morning) = 45%