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%

Question

Mathematics

Charlie Harrington

14 December, 01:37

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%

+2

Answers (1)

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Skylar Cooley · Answer 1

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%