# Engineering statistics, i need solutions in 15 minutes please. MCQ/Engineering c

Engineering statistics, i need solutions in 15 minutes please. MCQ/Engineering company has a task of checking compressive strength for 100 concrete cubes. The results revealed that 85 cubes passed the compressive strength test successfully and 15 cubes failed in the test. If 10 cubes are selected at random to be inspected by the company, determine the probability that the 8 cubes will pass the test and 2 cubes will fail in the test by using the Combinatorial Analysis.

A-0.6553

B-0.2919

C-0.3415

D-0.4522

E-0.1156

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Given:
Total number of cubes $$\displaystyle={100}$$
Number of cubes passed $$\displaystyle={85}$$
Number of cubes failed $$\displaystyle={15}$$
Number of cubes selected $$\displaystyle={10}$$
The probability that 8 cubes will pass the test and 2 cubes will fail in the test by using the Combinatorial Analysis is obtained as below:

P(8pass and 2 fail) $$\displaystyle={\frac{{_{85}{C}_{{{8}}}\times_{{{15}}}{C}_{{{2}}}}}{{_{100}{C}_{{{10}}}}}}$$
$$\displaystyle={0.2919}$$ Thus, the probability that 8 cubes will pass the test and 2 cubes will fail in the test is 0.2919.
Option B. 0.2919