Question

Given that events A and B are independent with P(A) = 0.86 andP(B|A) = 0.75, determine the value of P(B), rounding to the nearestthousandth, if necessary.B.Answer:Submit Answerattempt 2 out of 2Privacy Policy Terms of Service

Answer 1

SOLUTION

P(B/A) is the probability of B if A occurs. And this is given as

$\begin{gathered} P\mleft(B/A\mright)=\frac{P(A\cap B)}{P(A)} \\ \\ \text{From the question } \\ P(B/A)=0.75,\text{ }P(A)=0.86 \\ 0.75=\frac{P(A\cap B)}{0.86} \\ \\ P(A\cap B)=0.75\times0.86=0.645 \\ P(A\cap B)=P(A)\times P(B) \\ 0.645=0.86\times P(B) \\ P(B)=\frac{0.645}{0.86} \\ \\ P(B)=0.75 \end{gathered}$