Question

In a box containing 100 eggs, 10 eggs are rotten. The probability that out of a sample of 5 eggs none is rotten if the sampling is with replacement is

• A. $\left( \frac { 1 } { 10 } \right) ^ { 5 }$
• B. $\left( \frac { 1 } { 5 } \right) ^ { 5 }$
• C. $\left( \frac { 9 } { 5 } \right) ^ { 5 }$
• D. $\left( \frac { 9 } { 10 } \right) ^ { 5 }$

Answer 1

Answer: (D)

$\left( \frac { 9 } { 10 } \right) ^ { 5 }$

Answer 2

Let $P ($ fresh egg $) = \frac { 90 } { 100 } = \frac { 9 } { 10 } = p$

$P ($ rotten egg $) = \frac { 10 } { 100 } = \frac { 1 } { 10 } = q$ ; $n = 5$ $r = 5$

So the probability that none egg is rotten

$= { } ^ { 5 } C _ { 5 } \left( \frac { 9 } { 10 } \right) ^ { 5 } \cdot \left( \frac { 1 } { 10 } \right) ^ { 0 } = \left( \frac { 9 } { 10 } \right) ^ { 5 }$.