Total number of cubes \(\displaystyle={100}\)

Number of cubes passed the test successfully \(=85\)

Number of cubes failed in the test \(=15\)

It is given that if 10 cubes are selected at random to be inspected by the company then we have to find the probability that 8 cubes will pass the test and 2 cubes will fail in the test.

Total possible cases \(\displaystyle=^{{{100}}}{C}_{{{10}}}\)

Favorable cases \(\displaystyle=^{{{85}}}{C}_{{{8}}}\times^{{{15}}}{C}_{{{2}}}\)

Required probability \(=\frac{Favorable\ cases}{Total\ possible\ cases}\)

\(=\frac{^{85}C_{8}\times ^{15}C_{2}}{^{100}C_{10}}\)

\(\displaystyle={\frac{{{4.8125}\times{10}^{{{10}}}\times{105}}}{{{1.731}\times{10}^{{{13}}}}}}\)

\(\displaystyle={\frac{{{2.7801}\times{105}}}{{{1000}}}}\)

\(\displaystyle={\frac{{{291.92}}}{{{1000}}}}\)

\(\displaystyle={0.2919}\)

Thus, the required probability that 8 cubes will pass the test and 2 cubes will fail in the test is 0.2919.

Hence, option (e) is correct