According to a recent 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 News, 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?