Answer to Question #156958 in Statistics and Probability for DANIA

Question

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 70% of the time. If Base Construction Company does not bid on a job, the probability that Olive Construction Company will get the job is 0.50. If Base Construction Company does bid on a job, the probability that Olive Construction Company will get the job is 0.25.

(a)Draw the tree diagram

Answer 1

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

Thus here we have:

$P(B)=0.70$

$P(\bar{B})=1-P(B)=1-0.70=0.30$

$P(O|B)=0.25$

$P(O|\bar{B})=0.50$

$P(O\cap B)=P(O|B)P(B)=0.25(0.7)=0.175$

$P(O\cap\bar{B})=P(O|\bar{B})P(\bar{B})=0.50(0.3)=0.150$

Probability Table:

$\def\arraystretch{1.5} \begin{array}{c:c:c:c} & B & \bar{B}& \\ \hline O & 0.175 & 0.150 & 0.325\\ \hdashline \bar{O} & 0.525 & 0.150 & 0.675 \\ \hdashline & 0.700 & 0.300 & 1 \end{array}$

Venn diagram