Question

A man has 3 pairs of white socks and 2 pairs of blue socks kept together in a bag. If he dressed up hurriedly in the dark, the probability that after he has put on a white sock, he will then put on another white sock is `M/n` (`M/n` is in simplest form) then n – M = ______.

Options

• 2.00

• 3.00

• 4.00

• 5.00

Answer 1

A man has 3 pairs of white socks and 2 pairs of blue socks kept together in a bag. If he dressed up hurriedly in the dark, the probability that after he has put on a white sock, he will then put on another white sock is `M/n` (`M/n` is in simplest form) then n – M = 4.00.

Explanation:

E₁ = Event that he has put on white sock first

E₂ = Event that the second sock is also white.

`P(E_2/E_1) = (P(E_2 ∩ E_1))/(P(E_1))`

= `(""^6C_1 xx ""^5C_1)/(""^6C_1 xx ""^9C_1)`

= `5/9`

= `M/n`

∴ n – M = 4