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

Explanation

Let `R` be the event of being rich and `F` be the event of being famous.
Given that `P(R)=10/100= 0.1`
`P(F)=5/100=0.05`
`P(R∩F)=3/100=0.03`
Hence, the required probability`=P(R∩F')+P(R'∩F)`
`P(R∩F')+P(R'∩F)=P(R)+P(F)–2P(R∩F)`
Now, substitute the values.
Required probability:`=(0.1)+(0.05)–2(0.03)`
`= 0.1+0.05–0.06`
`=0.1–0.01`
`=0.09`
Hence, the probability of that a person picked at random from the population is either famous or rich but not both is `0.09`.