Problem 11 A graduating senior seeking a job has interviews with two companies.

Question

Problem 11

A graduating senior seeking a job has interviews with two companies. After the interviews, he estimates that his chance of getting an offer from the first company is 0.6. He thinks he has a 0.5 chance with the second company, and that the probability that at least one will reject him is 0.8. What is the probability that he gets at least one offer? About 10 percent of the population is left-handed. Of those who are right-handed, about 40 percent own dogs. If you were to select a person at random, what is the joint probability that the chosen person is a right-handed and does not own a dog? If A and B are two events, with neither being empty sets or the entire sample space, prove that if P(A|B) > P(A) then P(B|A)

Explanation / Answer

Let

A= getting an offer from the first company
B = getting an offer from the second company

We have , given that P(A) = 0.6 , P(B) =0.5 & P(not A or not B)= 0.8

And
P( A and B ) = 1 - P(not [A and B] ) =1-.8 =.2

So,the probability that he gets at least one offer
P( A or B) = P(A) + P(B) - P(A and B) = 0.5+.6-.2 = .9

So, answer is 0.9

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