Question

The weather report says that in the following 60 days, 24 days will be cloudy, 15 days will be rainy, and 10 days will be cloudy and rainy. Let event A
represent cloudy days and event B
represent rainy days. Are the events A
and B
independent or dependent, and why?(1 point)
Responses

dependent, because P(A)=P(B)

dependent, because upper P left parenthesis upper A right parenthesis equals upper P left parenthesis upper B right parenthesis

dependent, because P(A)≠P(B)

dependent, because upper P left parenthesis upper A right parenthesis does not equal upper P left parenthesis upper B right parenthesis

independent, because P(A and B)=P(A)⋅P(B)

independent, because upper P left parenthesis upper A and upper B right parenthesis equals upper P left parenthesis upper A right parenthesis times upper P left parenthesis upper B right parenthesis

dependent, because P(A and B)≠P(A)⋅P(B)

Answer 1

Dependent, because P(A and B) ≠ P(A)·P(B).

P(A)=24/60=0.4, P(B)=15/60=0.25, so P(A)·P(B)=0.4·0.25=0.10 (6/60), but P(A and B)=10/60≈0.1667. Since 10/60 ≠ 6/60, A and B are dependent.