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?

AYes. P(married | exercise in the morning) = P(exercise in the morning | married) = 75%
BYes. P(married and exercise in the morning) = P(married)·P(exercise in the morning) = 45%
CNo. P(married and exercise in the morning) = 60% & P(married)·P(exercise in the morning) = 42%
DNo. P(married and exercise in the morning) = 45% & P(married)·P(exercise in the morning) = 34.2%

Question

09-02-2016
Mathematics

Answered

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?

AYes. P(married | exercise in the morning) = P(exercise in the morning | married) = 75%
BYes. P(married and exercise in the morning) = P(married)·P(exercise in the morning) = 45%
CNo. P(married and exercise in the morning) = 60% & P(married)·P(exercise in the morning) = 42%
DNo. P(married and exercise in the morning) = 45% & P(married)·P(exercise in the morning) = 34.2%

Verified Answer :

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taskmasters taskmasters · Answer 1 · 2016-02-11T01:06:59-05:00

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%

kthegoat20 kthegoat20 · Answer 2 · 2020-01-08T13:28:33-05:00

kthegoat20 kthegoat20

08-01-2020

Answer:

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

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