A racial discrimination study found that 60% of the workers were white, 30% were

Question

A racial discrimination study found that 60% of the workers were white, 30% were black and 10% are other races. Given that a worker was white, the probability that the worker had claimed discrimination was 30%. Given that a worker was black, the probability that the worker had claimed discrimination was 40%. Given that a worker was another race, the probability that the worker had claimed discrimination was 0%. What is the probability that a randomly selected worker is black and had not claimed discrimination?

Explanation / Answer

Let

B = black
D = claimed discrimination

Hence

P(B n D') = P(B) P(D'|B) = 0.30*(1-0.40) = 0.18 [ANSWER]

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