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

Concept:

Binomial distribution

In n independent trials, if p and q are the probability of success and failure respectively then the probability of exactly r success = ⁿC_r p^r (q)^n-r

Explanation:

Given, During war, one ship out of 5 was sunk on an average in making a certain voyage

⇒ P(sinking) =   {failure}

⇒ P(safe arriving) =  P(not sinking) = 1 -  =   {success}

Now the probability that exactly 3 out of 5 ships would arrive safely = Probability of 3 success

 n = 5, p = , q = , r = 3

⇒ The probability that exactly 3 out of 5 ships would arrive safely =  5C3 ()3 ()5-3 

⇒ The probability that exactly 3 out of 5 ships would arrive safely =  

⇒ The probability that exactly 3 out of 5 ships would arrive safely =  

∴ The correct option is (4).