Question

Two events are independent. The P(A) = 0.34 and the P(A and B) = 0.085. What is the P(B)?(Express your answer as a decimal)

Answer 1

Hello there. To solve this question, we have to remember some properties about independent events and probabilities.

Given that the events A and B are independent and we know that

$\begin{gathered} P(A)=0.34\text{ and} \\ \text{ }P(A\text{ and }B)=P(A\cap B)=0.085 \end{gathered}$

We want to determine the value of P(B).

For this, remember that for independent events A and B,

$P(A\cap B)=P(A)\cdot P(B)$

Hence, we get that

$\begin{gathered} 0.085=0.34\cdot P(B) \\ \end{gathered}$

Divide both sides of the equation by a factor 0.34

$P(B)=\dfrac{0.085}{0.34}=0.25$

This is the answer to this question.