Question

The probability that Bryan goes to the store is 0.18. The probability that he goes to the movies is 0.34 . The probability that he goes to the store, given that he goes to the movies, is 0.46 . What is the probability he goes to the store or to the movies?a. 32.38 %b. 36.36%c.40 .28%d. 44.46%

Answer 1

Answer:

b. 36.36%

Explanation:

• The probability that Bryan goes to the store, P(S)= 0.18

,

• The probability that he goes to the movies, P(M)=0.34

,

• The probability that he goes to the store, ,given that, he goes to the movies, P(S | M)= 0.46

By Conditional Probability

$P(S|M)=\frac{P(S\cap M)}{P(M)}$

Therefore:

$\begin{gathered} 0.46=\frac{P(S\cap M)}{0.34} \\ P(S\cap M)=0.46\times0.34 \\ =0.1564 \end{gathered}$

The probability that he goes to the store or to the movies, P( S U M) is, therefore:

$\begin{gathered} P(S\cup M)=P(S)+P(M)-P(S\cap M) \\ =0.18+0.34-0.1564 \\ =0.3636 \\ =36.36\% \end{gathered}$

The correct choice is B.