Question

company A is determining whether it should submit a bid for a new shopping center. In the past, their main competitor, company B, has submitted bids 90% of the time. if company b does not bid on a job, the probability that company A will get the job is 0.20. if company B bids on job, the probability that company A will the job is 0.15. if company A gets the job, what is the probability that company B did not bid. What is the probability that company A will get the job?

Answer 1

Answer on 39160, Math, Statistics and Probability Probability that company A gets the job is

$$P(A) = P(B) \cdot P(B|A) + (1 - P(A)) \cdot P(\overline{B}|A) = 0.9 \cdot 0.15 + 0.1 \cdot 0.2 = 0.155$$

where $P(B)$ is probability that company B bids the job.

Now we will use Bayes' theorem. It says

$$P(B|A) = \frac{P(A|B)P(B)}{P(A)}$$

where $P(B|A)$ is posterior, probability that company had made the bid if we know that A got the job. So

$$P(B|A) = \frac{0.9 \cdot 0.15}{0.155} \approx 0.87$$