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According to a survey by two United Nations agencies and a nongovernmental organization, two in every three women in the Indian capital of New Delhi are likely to face some form of sexual harassment in a year (BBC World Nens, July 9, 2010). The study also reports that women who use public transportation are especially vulnerable. Suppose the corresponding probability of harassment for women who use public transportation is $0.82$. It is also known that $28 \%$ of women use public transportation.

a. What is the probability that a woman takes public transportation and also faces sexual harassment?

b. If a woman is sexually harassed, what is the probability that she had taken public transportation?

Solution

VerifiedIn this exercise, we need to find the probability of a woman who takes public transportation and is facing sexual harassment and the probability of a woman taking public transport if she was sexually harrassed.

The exercise states that two in three woman face a sexual harassment in a year ($P(S)=\frac{2}{3}$). $28\%$ of woman use public transportation ($P(T)=0.28$) and the probability of harassment of a woman who takes public transportation is $0.82$ ($P(S|T)=0.82$).

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