Engineering
Mathematics
Basic Definitions Related to Probability
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
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Solution
R : rich people F : Famous people
P(R) = 10 / 100 = 0.1, P(F) = 5 / 100 = 0.05
P(R⋂F) = 3 / 100 = 0.03
(i) Rich but not famous
P(R⋂F') = P(R) – P(R⋂F)
(ii) Famous but not Rich
P(F⋂R') = P(F) – P(R⋂F)
Required Probability = P(R⋂F') + P(F⋂R')
= P(R) + P(F) –2 × P(R⋂F)
= 0.1 + 0.05 – 2 × 0.03 = 0.09