Answer to Question #201151 in Statistics and Probability for LULA

Question

able building company is deciding whether to submiit a bid to build a new shopping centre. In the past, ABC's main competitor, Big Building Company (BBC) has submitted bids 70% of the time. If BBC does not bid for a job, the probability that ABC will get the job is 50%. If BBC bids on a job, the probability that ABC will get the job reduces to 25%. What is the probability that ABC will get the job?

Answer 1

Let $A$ be the event ''ABC will get the job'', $B$ be the event '' BBC bids on a job''.

Given $P(B)=0.7. P(\bar{B})=1-0.7=0.3,$

$P(A|B)=0.25. P(A|\bar{B})=1-0.7=0.5$

The Law of Total Probability

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

$$=0.25(0.7)+0.5(0.3)=0.325$$

The probability that ABC will get the job is 0.325.