What is the probability that: (a) Both positions will be filled by women? (b) At

Question

What is the probability that: (a) Both positions will be filled by women? (b) At least one of the positions will be filled by a woman? (c) Neither of the positions will be filled by a woman? There are 300 homes in a neighborhood. At 100 of these, on a certain evening, no one is at home. Of the remaining homes, the occupants of 50 will not participate in telephone surveys. On a particular evening, a person conducting a telephone survey calls one of these homes at random. What is probability that: (a) The surveyor will call a home where no one is present? (b) The surveyor will call a home in which someone is present, but the person will not participate in the survey? (c) The call will result in participation in the survey? In a large city, 70% of the households receive a daily newspaper, and 90% have a television set. Suppose that these two events are independent. What is the probability that a randomly selected household will be one that receives a daily newspaper and has a television set?

Explanation / Answer

12 ) a) as there are 100 out of 300 home where no one is present; hence probability=100/300=1/3

b)as there are 200 homes where somebody is present out of which 50 will not participate in survey;

hence probability =50/200=1/4

c) there are 150 homes out of 300 who will participate ; hence probabilty =150/300=1/2

probabilty that household receives newspaper and has a television set =0.7*0.9=0.63

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