Question

From past experience it is known that an investor will invest in security $A$ with a probability of $0.6$, will invest in security $B$ with a probability $0.3$and will invest in both $A$ and $B$with a probability of $0.2$. What is the probability that an investor will invest neither in $A$ nor in $B$?

• A. $0.7$
• B. $0.28$
• C. $0.3$
• D. $0.4$

Answer 1

The correct option is C

$0.3$

Explanation for the correct option:

Find the required probability:

Probability of an investor will invest in security $A$ is $P\left(A\right)=0.6$

Probability of an investor will invest in security $B$ is $P\left(B\right)=0.3$

Probability of an investor will invest in both $A$ and $B$ is $P\left(A\cap B\right)=0.2$

As we know,

$\mathit{P}\left(A\cup B\right)\mathbf{}\mathbf{=}\mathbf{}\mathit{P}\mathbf{\left(}\mathit{A}\mathbf{\right)}\mathbf{+}\mathit{P}\mathbf{\left(}\mathit{B}\mathbf{\right)}\mathbf{-}\mathit{P}\left(A\cap B\right)$

$=0.6+0.3-0.2$

$=0.7$

$\therefore P$(neither $A$ nor $B$) $=1-P\left(A\cup B\right)$

$=1-0.7$

$=0.3$

Thus, the probability that an investor will invest neither in $A$ nor in $B$ is $\mathbf{0}\mathbf{.}\mathbf{3}$

Hence, Option ‘C’ is Correct.