Answer to Question #151621 in Statistics and Probability for Parviz

Question

The Olive Construction Company is determining whether it should submit a bid for a new shopping center. In the past , Olive’s main competitor , Base Construction Company ,has submitted bids 80% of the time. If Base Construction Company does not bid on a job ,the probability that the Olive Construction Company will get the job is 0.50. If Base Construction Company does bid on a job, the probability that the Olive Construction Company will get the job is 0.25. If the Olive Construction Company will get the job, what is probability that, Base Construction Company did not bid?

Answer 1

Let's denote A for Base Construction Company submits bids on a job and B for Olive Construction Company getting the job.

Thus here we have:

the probability of submitting bids is 80%:

$P(A)=0.8$

the probability that the Olive Construction Company will get the job given that Base Construction Company does not bid on a job is 0.5:

$P(B|\bar A)=0.5$

the probability that the Olive Construction Company will get the job given that Base Construction Company does bid on a job is 0.25:

$P(B|A)=0.25$

We need to find the probability that Base Construction Company did not bid given that the Olive Construction Company will get the job:

$P(\bar A|B)$

Using Bayes Theorem we have:

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

where $P(\bar A) = 1-P(A)=1-0.8=0.2$

Therefore

$$P(\bar A|B)=\frac{0.5\cdot0.2}{0.5\cdot0.2+0.25\cdot0.8}=0.33$$

Answer: If the Olive Construction Company will get the job, the probability that Base Construction Company did not bid is 0.33.