Question

If P(A) = 0.24, P(B) = 0.52, and A and B are independent events, what is P(A or B)?

a. $0.1248$

b. $0.28$

c. $0.6352$

d. $0.76$

e. The answer cannot be determined from the information given.

Short answer

The required answer is $0.6352$

The correct option is$\left(c\right)$

Step-by-step solution

Given information

$P\left(A\right)=0.24,P\left(B\right)=0.52,A$and $B$are independent.

Explanation

Because $A$and $B$are separate events,

$$\begin{gathered} P\left(A{\hat{a}}^{\wedge }\mathrm{a}B\right)=p\left(A\right)P\left(B\right)=0.24(0.52)=0.1248 \\ P\left(A{\hat{a}}^{\wedge }\mathrm{B}\right)=\mathrm{P}\left(\mathrm{A}\right)+\mathrm{P}\left(\mathrm{B}\right)-\mathrm{P}\left({\mathrm{Aâ}}^{\wedge }\odot \mathrm{B}\right) \\ =0.24+0.52-0.1248 \\ =0.6352 \end{gathered}$$

Therefore, the option $\left(c\right)$is correct.