Question

A report describes the results of a large survey involving approximately 3500 people that was conducted for the Center for Disease Control. The sample was selected in a way that the Center for Disease Control believed would result in a sample that was representative of adult Americans. One question on the survey asked respondents if they had learned something new about a health issue or disease from a TV show in the previous 6 months. Data from the survey was used to estimate the following probabilities, where L = event that a randomly selected adult American reports learning something new about a health issue or disease from a TV show in the previous 6 months and F = event that a randomly selected adult American is female P(L) = 0.51 P(L ∩ F) = 0.38 Assume that P(F) = 0.5. Are the events L and F independent events? Use probabilities to justify your answer

L and F are / are not independent events, because

P(L) · P(F) =  ,

which is/ is not equal to P(L ∩ F).

Answer 1

L and F are not independent events, because

P(L)*P(F)=0.51*0.5=0.255 ;

which is not equal to P(L ∩ F)