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

Question

Dr. Abubacker · Accepted Answer

(c)
Let $P(R) = 10\% = \frac{1}{10}$
$P(F) = 5\% = \frac{1}{20}$
$P(R \cap F) = 3\% = \frac{3}{100}$
Probability of getting either rich or famous but not both
$= P\left( R \cap F^{'} \right) + P(R^{'} \cap F)$
$= P(R) - P(R \cap F) + P(F) - P(R \cap F)$
$= P(R) + P(F) - 2P(R \cap F)$
$= \frac{1}{10} + \frac{1}{20} - \frac{6}{100} = \frac{10 + 5 - 6}{100} = 0.09$

Q. 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

Explanation

Reviewed by Dr. Abubacker

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