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)

\(\displaystyle={P}{\left({A}\cap{C}\right)}+{P}{\left({B}\cap{C}\right)}\)

\(\displaystyle={P}{\left({A}\right)}{P}{\left({C}{\mid}{A}\right)}+{P}{\left({B}\right)}{P}{\left({C}{\mid}{B}\right)}\)

\(\displaystyle={0.85}{\left({0.60}\right)}+{0.15}{\left({0.40}\right)}\)

\(\displaystyle={0.57}\)

Answer: 0.57

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)

\(\displaystyle={P}{\left({A}\cap{C}\right)}+{P}{\left({B}\cap{C}\right)}\)

\(\displaystyle={P}{\left({A}\right)}{P}{\left({C}{\mid}{A}\right)}+{P}{\left({B}\right)}{P}{\left({C}{\mid}{B}\right)}\)

\(\displaystyle={0.85}{\left({0.60}\right)}+{0.15}{\left({0.40}\right)}\)

\(\displaystyle={0.57}\)

Answer: 0.57