Question

If $P(\mathrm{A})=0.24$and $P(\mathrm{B})=0.52$and events $\mathrm{A}$and $\mathrm{B}$are independent, what is $P(\mathrm{A}$or $\mathrm{B})$?

а. $0.1248$

b. $0.28$

c. $0.6352$

d.$0.76$

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

Short answer

Correct option is

$c.0.6352$

Step-by-step solution

Given information

Given in the question that, We need to find $P(A$or $B)$ if role="math" localid="1654186447547" $P(\mathrm{A})=0.24$and role="math" localid="1654186458189" $P(\mathrm{B})=0.52$and events $\mathrm{A}$and $B$are independent.

Explanation

This is a given,

$P\left(A\right)=0.24$

$P\left(B\right)=0.52$

As a result, for independent events, use the multiplication rule:

$P(\mathrm{A}\text{and}\mathrm{B})=P\left(A\right)\times P\left(B\right)$

$=0.24\times 0.52$

$=0.1248$

Now that we've got that,

$P(\mathrm{A}\text{or}\mathrm{B})=P\left(A\right)+P\left(B\right)-P(\mathrm{A}\text{and}\mathrm{B})$

$=0.24+0.52-0.1248$

$=0.6352$

As a result, option (c) is the proper choice.