Answer with explanationformula please A recent graduate from

Answer with explanation/formula please

A recent graduate from Brock U has applied for a job with Royal Bank of Canada and CIBC. The graudate feels that she has a 70% chance of receiving an offer from RBC and a 60% chance of receiving an offer from CIBC. If she receives an offer from CIBC, she believes that she has an 80% chance of receiving an offer from RBC.

1. what is the prob that both banks will make her an offer
2. what is the prob that at least one bank will make her an offer
3. given that rbc has made the graduate an offer, what is the prob that cibc will make her an offer?

Solution

let A be the event that RBC will make her an offer

B be the event that CIBC will make her an offer

given that P[A]=0.7   P[B]=0.6   P[A|B]=0.8

1. P[both banks will make her offer]=P[A and B]=P[A|B]*P[B]=0.8*0.6=0.48 [answer]

2. P[at least one bank will make her offer]=P[A or B]=P[A]+P[B]-P[A and B]=0.7+0.6-0.48=0.82 [answer]

3. here we need to find P[B|A]=P[A and B]/P[A]=0.48/0.7=0.6857 [answer]