Question

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

Options

• `(1/10)^5`

• `(1/5)^5`

• `(9/5)^5`

• `(9/10)^5`

Answer 1

In a box containing 100 eggs, 10 eggs are rotten. The probability that out of a sample of 5 eggs none are rotten, if the sampling is with replacement, is `underline((9/10)^5)`.

Explanation:

Probability of getting rotten egg is

p = `10/100 = 1/10`

∴ q = `1 - 1/10 = 9/10`

Also, n = 5

∴ The probability that no egg is rotten is

P(X = 0) = `"^5C_0 (1/10)^0 (9/10)^5(9/10)^5`