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%
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%
