Question

one ship out of 10 was sunk on an average in making certain voyage. find tha probability that out of 5 ships , 4 would arrive safely​

Answer 1

Given:

One ship out of 10 was sunk on an average in making certain voyage.

⇒ q = 1/10 and p = 9/10

To find:

The probability that out of 5 ships , 4 would arrive safely​

Solution:

We need to find P(X ≥ 4)

From given we have,

P(X ≥ 4) = P(X = 4) + P(X = 5)

P(X ≥ 4) = $^5C_4\left ( \dfrac{9}{10} \right )^4\left ( \dfrac{1}{10} \right )^1 + ^5C_5\left ( \dfrac{9}{10} \right )^4\left ( \dfrac{1}{10} \right )^0$

P(X ≥ 4) $=5 \times \left ( \dfrac{9}{10} \right )^4\left ( \dfrac{1}{10} \right ) + 1 \times \left ( \dfrac{9}{10} \right )^4$

P(X ≥ 4) = 0.328 + 0.590

P(X ≥ 4) = 0.918

Therefore, the probability that out of 5 ships , 4 would arrive safely​ is 0.918