Question : A person can hit a target 5 times out of 8 shots. If he fires 10 shots, what is the probability that he will hit the target twice?
Option 1: $\frac{1135 \times 3^8}{8^{10}}$
Option 2: $\frac{1165 \times 3^8}{8^{10}}$
Option 3: $\frac{1175 \times 3^8}{8^{10}}$
Option 4: $\frac{1125 \times 3^8}{8^{10}}$
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Correct Answer: $\frac{1125 \times 3^8}{8^{10}}$
Solution : Probability of hitting = $\frac{5}{8}$ Probability of losing = $\frac{3}{8}$ Probability of hitting twice when 10 shots are fired = 10 C 2 $(\frac{5}{8})^2(\frac{3}{8})^8$ = $\frac{10×9×5×5}{1×2}$× $\frac{ 3^8}{8^{10}}$ = $\frac{1125 ×3^8}{8^{10}}$ Hence, the correct answer is $\frac{1125 ×3^8}{8^{10}}$.
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