Awomen-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%