student is graduating from their university and has applied to jobs at company A and B. The student thinks they have a 40 % chance of a receiving an offer from company A and a 50 % chance of receiving an offer from company B. If the student receives an offer from company A, the student believes they have a 70 % chance of receiving an offer from company B.
(a) What is the probability that both companies will make the student an offer?
(b) What is the probability that at least one company will make the student an offer.
(c) If the student receives an offer from company A, what is the probability she will not receive an offer from company B?
60%
To find the probabilities in this scenario, we can use the concept of conditional probability and apply it to the given information. Let's break down each part of the question:
(a) What is the probability that both companies will make the student an offer?
To find the probability that both companies will make the student an offer, we need to multiply the individual probabilities together.
P(offer from A and offer from B) = P(offer from A) * P(offer from B | offer from A)
P(offer from A) = 0.40 (given)
P(offer from B | offer from A) = 0.70 (given)
P(offer from A and offer from B) = 0.40 * 0.70 = 0.28
So, the probability that both companies will make the student an offer is 0.28 or 28%.
(b) What is the probability that at least one company will make the student an offer?
To find the probability that at least one company will make an offer, we need to consider the complement event. The complement event in this case would be the student not receiving an offer from both companies.
P(at least one offer) = 1 - P(no offer from A and no offer from B)
P(no offer from A) = 1 - P(offer from A) = 1 - 0.40 = 0.60 (complement event)
P(no offer from B | no offer from A) = 1 - P(offer from B | offer from A) = 1 - 0.70 = 0.30 (complement event)
P(no offer from A and no offer from B) = P(no offer from A) * P(no offer from B | no offer from A)
P(no offer from A and no offer from B) = 0.60 * 0.30 = 0.18
P(at least one offer) = 1 - 0.18 = 0.82
So, the probability that at least one company will make an offer is 0.82 or 82%.
(c) If the student receives an offer from company A, what is the probability she will not receive an offer from company B?
To find this probability, we need to use the conditional probability of not receiving an offer from B given that an offer was received from A.
P(not offer from B | offer from A) = 1 - P(offer from B | offer from A) = 1 - 0.70 = 0.30
So, if the student receives an offer from company A, the probability that she will not receive an offer from company B is 0.30 or 30%.