Question

Construction company A is determining whether it should submit a bid for a new shopping center. In the past, their main competitor construction company B, has submitted bids 90% of the time. Y company B does not bid on a job, the probability that company A will get the job is 0.60. f company B bids on a job the probability that company A will get the job is 0.25 a. If company A gets the job, what is the probability that company B did not bid? b. What is the probability that company A will get the job? a. If company A gets the job, what is the probability that company B did not bid? (Round to three decimal places as needed) b. What is the probability that company will get the job? Round to three decimal poom as needed)

Answer 1

Solution

$\bar{B}$ 10%

B 90%

A $\rightarrow$ A get the job

We have

P($\bar{B}$ ) =0.10 , P(A/ $\bar{B}$ ) =0.60

P(B ) =0.90 ,   P(A/ B ) =0.25

P(A) = P($\bar{B}$ ) *P(A/ $\bar{B}$ ) + P(B ) * P(A/ B )

= 0.10 *0.60+ 0.90*0.25

= 0.060 + 0.225

= 0.285

(a) P ($\bar{B}$/A ) =     $\frac{P( \bar{B}) *P(A/ \bar{B} )}{ P( \bar{B}) *P(A/ \bar{B} ) + P(B ) * P(A/ B ) }$

P ($\bar{B}$/A ) = $\frac{P( \bar{B}) *P(A/ \bar{B} )}{ P( \bar{B}) *P(A/ \bar{B} ) + P(B ) * P(A/ B ) } =\frac{0.060}{0.285}$

P ($\bar{B}$/A ) = 0.211 Answer

(b) P(A) = 0.285 Answer