Question

In a certain population $10\%$ of the people are rich, $5\%$ are famous and $3\%$ are rich and famous. The probability that a person picked at random from the population is either famous or rich but not both is equal to

• A. $0.07$
• B. $0.08$
• C. $0.09$
• D. $0.12$

Answer 1

The correct option is C

$0.09$

Explanation of the correct option :-

Finding the probability:

Number of people who are rich $=10\%$

Let $\mathrm{R}$ be the event of being rich

$\mathrm{P}\left(\mathrm{R}\right)=0.1$

No. of people who are famous $=5\%$

Let $\mathrm{F}$ be the event of being famous

$\mathrm{P}\left(\mathrm{F}\right)=0.05$

No. of people who are rich and famous both $=3\%$

$\mathrm{P}(\mathrm{R}\cap \mathrm{F})=0.03$

The probability of the person picked from the population is either rich or famous but not both $=\mathrm{P}(\mathrm{R}\text{'}\cap \mathrm{F})+\mathrm{P}(\mathrm{R}\cap \mathrm{F}\text{'})$

$=\mathrm{P}\left(\mathrm{R}\right)+\mathrm{P}\left(\mathrm{F}\right)-2\mathrm{P}(\mathrm{R}\cap \mathrm{F})$

$=0.1+0.05-0.06$

$$\begin{gathered} =0.1-0.01 \\ =0.09 \end{gathered}$$

Hence the correct option is C.