Two companies A and B consider making an offer for road cons

Two companies A and B consider making an offer for road construction. The company A makes the submission. The probability that B submits the proposal is 1/3. If B does not submit the proposal, the probability that A gets the job is 3/5. If B submits the proposal, the probability that A gets the job is 1/3. What is the probability that A will get the job?

Solution

We will use the total probability law to find the required probability.

P(A will get the JOB) = P(B submits the proposal)*P(A gets the job when B submits the proposal)+P(B does not submit the proposal)*P(A gets the JOB when B does not submit the proposal)

P(A will get the JOB) = (1/3)(1/3)+(1-1/3)(3/5) = 1/9 + 2/5 = 23/45 = 0.51