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 $0.09$

R: rich people F:Famous people

P(R)=10/100=0.1 ,P(F)=5/100=0.05

P(R$\cap$F)=3/100=0.03

i) Rich but not famous

P(R$\cap$F')=P(R)-P(R$\cap$F )

i) Famous but not Rich

P(F$\cap$R')=P(F)-P(R$\cap$F )

Required Probability=P(R$\cap$F')+P(F$\cap$R')

=P(R)+P(F)-2*P(R$\cap$F)

=0.1+0.05-2*0.03=0.09