Question

Let Events A and B be described as follows:• P(A) = buying popcorn• P(B) = watching a movieThe probability that you watch a movie this weekend is 48% The probability of watching amovie this weekend and buying popcorn is 38%. If the probability of buying popcorn is 42%,are watching a movie and buying popcorn independent?

Answer 1

Given that;

`\begin{gathered} P(A)=42\%=0.42 \\ P(B)=48\%=0.48 \\ P(A\cap B)=38\%=0.38 \end{gathered}`

To find out if watching a movie and buying a popcorn are independent, the formula is

`\begin{gathered} P(A|B)=(P(A\cap B))/(P(B))=(0.38)/(0.48)=0.79166 \\ P(A|B)=0.79\text{ \lparen two decimal places\rparen} \end{gathered}`

From the deductions above;

Hence, the answer is

`No,\text{ because }P(A|B)=0.79\text{ and the }P(A)=0.42\text{ are not equal}`