During war one ship out of 5 was sunk on an average in making a certain voyage. What is the probability that <strong>EXACTLY</strong> 3 out of 5 ships would arrive safely?

Explanation

The probability of a ship arriving safely is p = 4/5, and sinking is q = 1/5. The probability of exactly 3 out of 5 ships arriving safely follows the binomial distribution: C(5,3) p^3 q^2 = 10 (4/5)^3 (1/5)^2 = 10 \times \frac{64}{125} \times \frac{1}{25} = \frac{128}{625}.

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