Question

If $\text{A}$ and $\text{B}$ are two independent events such that $\text{P(A) = 0.40, P(B) = 0.50.}$ Find $\text{P(neither A nor B)}$

• A. $0.90$
• B. $0.10$
• C. $0.2$
• D. $0.3$

Answer 1

The correct option is D

$0.3$

Explanation for the correct option

Step $\mathbf{1}$. Find $\mathbf{\text{P}}\left(\text{A'}\right)$ and $\mathbf{\text{P}}\left(\text{B'}\right)$:

Given,

$\text{P(A) = 0.40}$

$\text{P(B) = 0.50}$

We know that,

$\text{P(A') = 1- P}\left(\text{A}\right)$ $=$$1-0.4$$=$$0.6$

$\text{P(B') = 1- P}\left(\text{B}\right)$ $=$$1-0.5$$=$$0.5$

Step $2$. Find $\mathbf{\text{P}}\mathbf{\left(}\mathbf{\text{A'∩B'}}\mathbf{\right)}$:

We know that,

$\mathbf{\text{P}}\mathbf{\left(}\mathbf{\text{A'∩B'}}\mathbf{\right)}$$=$$\mathbf{\text{P}}\left(\text{A'}\right)\mathbf{\text{·P}}\left(\text{B'}\right)$

$=$$0.6$$\times$$0.5$

$\mathbf{\therefore }$ $\mathbf{\text{P}}\mathbf{\left(}\mathbf{\text{A'∩B'}}\mathbf{\right)}$$\mathbf{=}$ $\mathbf{0}\mathbf{.}\mathbf{3}$

Hence, option $\mathbf{"}\mathbf{\text{D"}}$ is correct.