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July 9th, 2014, 03:34 PM   #1
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Explanation Required with Probability Question(s)

Two questions which I am having a hard time understanding:

1. In a population of students, it was observed that 50% used radios with headphones and 50% never used headphones. Health officials reported that 35% of the students have severe hearing problems, 40% have moderate hearing problems and the remainders have no hearing problems. It is also observed that 50% students using headphones have severe hearing problems and 30% of students using headphones have moderate hearing problems.

a) Find the probability that a person has no hearing problem knowing that this person does not use radio with headphones?

b) Find the probability that a person does not use headphones knowing that this person does not have a hearing problem?


2. A commuter owns two cars, one a compact car and one a standard model. About 75% of the time he uses the compact to travel to work, and 25% of the time the standard model. When he uses the compact car he gets home by 5:30 about 75% of the time. If he uses the standard car, he gets home by 5:30 about 60% of the time. If he gets home at 5:35Pm, what is the probability that he used the compact car?



Any help is appreciated.
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