Question

A report describes the results of a large survey that was conducted for the Center for Disease Control (CDC). The sample was selected in a way that the CDC 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 = outcome 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 = outcome that a randomly selected adult American is female
Data from the survey were used to estimate the following probabilities:

P(L)= 0.58 P(F)= 0.50 P(L and F)= 0.31

Are the outcomes L and F independent? Use probabilities to justify your answer.

Answer 1

Since
`P(L \cap F) \\eq P(L)P(F)`, the outcomes L and F are not independent.

Explanation:

Independent events:

Two events, A and B are independent, if:

`P(A \cap B) = P(A)P(B)`

Are the outcomes L and F independent?

We are given that:

`P(L \cap F) = 0.31`

Multiplication of the probabilities:

`P(L)P(F) = 0.58*0.5 = 0.29`

Since
`P(L \cap F) \\eq P(L)P(F)`, the outcomes L and F are not independent.