1. Peter applied for a job at an accounting firm and a consulting firm. He knows that 50% of similarly qualified applicants receive job offers from the accounting firm; only 40% of similarly qualified applicants receive job offers from the consulting firm Peter also knows that 60% of similarly qualified applicants receive an offer from one firm or the other. Hints: A

75%

Explanation:

Assume that:

X is the probability that the Peter, qualified accountant would receive offer from the accounting firm AND

Y is the probability that the Peter, qualified accountant would receive offer from the consulting firm.

Here,

P(X) is 50%, P(Y) is 40% and P(X∪Y) is 60%

Now we want to find P(X/Y) = ?

We also know that:

P(X/Y) = P(X∩Y) STEP1 /  P(Y)

By putting values, we have:

P(X/Y) = 0.3 / 0.4 = 0.75 = 75%

Step 1: Find P(X∩Y)

P(X∪Y) = P(X) + P(Y)  -   P(X∩Y)

This implies that:

P(X∩Y) = P(X)  +  P(Y)  -   P(X∪Y)

By putting values we have:

P(X∩Y) = 0.5 + 0.4   -  0.6   =  0.3

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