# A construction company is currently bidding a job overseas in country

A construction company is currently bidding a job overseas in country X. The chance of winning the job depends on the current election results in country X. If party A wins the election, the chance of the company winning the job is 60%; otherwise ,there is only a 20% chance that the company will win the job. On the other hand, from poll data, the probability that party A will win the election is 0.85. compute the probability of the company's success in winning the job.

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Step 1
Let us denote the event of winning the job by C.
$$\displaystyle{A}=$$ the event that party A wins
$$\displaystyle{B}=$$ the event that party A does not win
Given that $$\displaystyle{P}{\left({C}{\mid}{A}\right)}={60}\%={0.60}$$
$$\displaystyle{P}{\left({C}{\mid}{B}\right)}={1}-{0.60}={0.40}$$
$$\displaystyle{P}{\left({A}\right)}={0.85}$$
$$\displaystyle{P}{\left({B}\right)}={1}-{0.85}={0.15}$$
Step 2
The probability of the company's success in winning the job is:
P(C)
$$\displaystyle={P}{\left({A}\cap{C}\right)}+{P}{\left({B}\cap{C}\right)}$$
$$\displaystyle={P}{\left({A}\right)}{P}{\left({C}{\mid}{A}\right)}+{P}{\left({B}\right)}{P}{\left({C}{\mid}{B}\right)}$$
$$\displaystyle={0.85}{\left({0.60}\right)}+{0.15}{\left({0.40}\right)}$$
$$\displaystyle={0.57}$$
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