What is the Probability Bob Receives a Job Offer in LA from a Large Firm?

[needhelp83]

Bob would like to go to either consulting or investment banking and will receive exactly one job offer in one of the industries mentioned. He thinks the probability of getting job in consulting to be 0.6 and investment baning to 0.4. He is interviewing with a small firm and a large firm for both investment banking and consulting. If he is offered an investment job, he believes the probability of getting offer from large firm is 0.8. If he is offered a consulting job he believes the probability of getting an offer from a large firm is 0.9

Bob knows that he will be in New York or Los Angeles. If he gets investment banking from small firm he will in up in New York with probability of 0.7; if he gets offer from a large investment bank he will definitely go to New York. If he is offered a consulting job he believes it will be equally likely to be in New York or Los Angeles regardless of firm.

1) Given that Bob is offered an investment banking job in New York, he assigns a probability of p of receiving an offer from the small firm. What is p?

To solve p I multiplied 0.4*.2*0.7= .056

2) Given that Bob is offered a job from a large firm, he assigns a probability q, of receiving a job offer in LA. What is q?

Unsure of what to do to solve for q

I know if he did Invest - Large - LA the probability would be 0
If he did consult - large - LA it would be 0.6*0.9*.5 = .27, but I don't think the question is asking for this.

 

[mighty2000]

To solve q, we need to consider the different scenarios in which Bob could receive a job offer from a large firm. These are:

1. Bob gets offered an investment banking job from a large firm and ends up in New York (with probability 0.4*0.8 = 0.32)
2. Bob gets offered an investment banking job from a large firm and ends up in Los Angeles (with probability 0.4*0.2 = 0.08)
3. Bob gets offered a consulting job from a large firm and ends up in New York (with probability 0.6*0.9 = 0.54)
4. Bob gets offered a consulting job from a large firm and ends up in Los Angeles (with probability 0.6*0.1 = 0.06)

Since we know that Bob has been offered a job from a large firm, the total probability of these scenarios must add up to 1. Therefore, we can set up the following equation:

0.32q + 0.08(1-q) + 0.54q + 0.06(1-q) = 1

Solving for q, we get q = 0.75. Therefore, Bob assigns a probability of 0.75 of receiving a job offer in Los Angeles if he is offered a job from a large firm.