Question

$\text{If A and B are two events such that P(A) = 0.4, P(A + B) = 0.7 and P(AB) = 0.2, then P(B) =?}$

• A. $0.1$
• B. $0.3$
• C. $0.5$
• D. $\text{None of these}$

Answer 1

The correct option is C

$0.5$

$$\begin{gathered} \text{Given data :} \\ \text{P(A) = 0.4} \\ \text{P(A + B) = 0.7 and} \\ \text{P(AB) = 0.2} \\ \text{We know that,} \\ \text{P(A+B) = P(A) + P(B) – P(AB)} \\ \text{⇒ 0.7 = 0.4 + P(B) – 0.2} \\ \Rightarrow \text{P(B) = 0.7 – 0.4 + 0.2} \\ \text{= 0.9 – 0.4} \\ \text{= 0.5} \\ \mathbf{\text{Hence, P}}\left(\text{B}\right)\mathbf{\text{= 0.5}} \end{gathered}$$