A person has applied for positions at Company A, Company B, and Company C. The p

Question

A person has applied for positions at Company A, Company B, and Company C. The probability of obtaining an offer from Company A is 0.4, from Company B is 0.3, and from Company C is 0.6. Assume that the three job offers will be independent. 2 marks a. What is the probability that the person will receive job offers from all three companies? 2 marks b. What is the probability that the person will receive a job offer from Company B only? 2 marks c. What is the probability that the person will receive a job offer from at least one of the three companies? 4 marks d. What is the probability that the person will receive exactly one job offer from the three companies? Hint: Construct a tree diagram.

Explanation / Answer

Solution:-

probability of getting a position at company A is equal to 0.4
probability of getting a position at company B is equal to 0.3
probability of getting a position at company C is equal to 0.6
probability of NOT getting a position at company A is equal to 1 - 0.4 = .6
probability of NOT getting a position at company B is equal to 1 - 0.3 = .7
probability of NOT getting a position at company C is equal to 1 - 0.6 = .4

a. p(A) * p(B) *p(C) = .4 * .3 * .6 = .072

b. p(B) * p(!A) * p(!C) = .3 * .6 * .4 = .072

c. That probability is 0.6 x 0.7 x 0.4 = 0.168.
That means the probability they get an offer from at least one is 0.832.

d. Either get a job from A only: 0.4 x 0.7 x 0.6 = 0.168
Or get a job from B only: 0.6 x 0.3 x 0.4 = 0.072
Or get a job from C only: 0.6 x 0.7 x 0.6 = 0.252
The answer is the sum of all three: 0.168 + 0.072 + 0.252 = 0.492

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