The probability of a randomly selected employee of a company being male is 60%. The probability of the employee being less than 30 years old is 70%. If the probability of the employee being less than 30 years old given that the employee is a male is 40%, what is the probability that the employee is a male, given that the employee is less than 30 years old?

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anonymous · Answer

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kirbykirby · Answer

Everything is almost good until the last step^. When you do $$P(male|<30)=\frac{P(male \cap <30)}{P(<30)} $$
We can't necessarily assume that $P(male \cap <30) =P(male)P(<30)$

Instead, you are given in the problem:
$$=0.4= P(<30|male)=\frac{P(<30 \cap male)}{P(male)}=\frac{P(<30 \cap male)}{0.6}$$
So $$ \frac{P(<30 \cap male)}{0.6}=0.4$$ $ \implies P(<30 \cap male)=0.4 \times 0.6 =0.24$

Thus,$$P(male|<30)=\frac{P(male \cap <30)}{P(<30)} =\frac{0.24}{0.7}=\frac{12}{35}=0.3429$$