Answer to Question #121299 in Statistics and Probability for hammad

Question

A students is going to graduate from a business department of a university by the end of the
semester. After being interviewed at two companies he likes, he assesses that his probability of
getting an offer from company A is 0.6, and his probability of getting an offer from company B is
0.45. If he believes that the probability that he will get offers from both companies is 0.35, what
is the probability that he will get at least one offer from these two companies?

Answer 1

Let A be the event that the student will get an offer from company A

and B be the event that the student will get an offer from company B

Then A $\cap$ B is the event that he will get offers from both companies

We are given,

P(A) = 0.6, P(B) = 0.45 and P(A $\cap$ B) = 0.35

$\therefore$ The probability that he will get at least one offer from these two companies is

P(A $\cup$ B) = P(A) + P(B) - P(A $\cap$ B) = 0.6 + 0.45 - 0.35 = 0.7

Answer: The probability that the student will get at least one offer from these two companies is 0.7.