Question

A drawer contains four pairs of socks, with each pair a different color. One sock at a time is randomly drawn from the drawer until a matching pair is obtained.

Calculate the probability that the maximum number of draws is required.

1. 0.0006

2. 0.0095

3. 0.0417

4. 0.1429

5. 0.2286

Answer 1

Maximum draws will be required if one draws each sock of different color in first 4 picks and the 5th pick would make the pair

P[ Maximum number of draws ] = P[ drawing any 1 type of socks from 4 ]*P[ drawing 1 out of remaining 3 ]*P[ drawing 1 out of remaining 2 ]*P[ drawing 1 out of remaining 1 ]

P[ drawing any 1 type of socks from 4 ] = 1/4

P[ drawing 1 out of remaining 3 ] = 1/3

P[ drawing 1 out of remaining 2 ] = 1/2

P[ drawing 1 out of remaining 1 ] = 1

P[ Maximum number of draws ] = (1/4)*(1/3)*(1/2)*1

P[ Maximum number of draws ] = 1/24

P[ Maximum number of draws ] = 0.0417