Question

In a sock drawer, you have a pair of blue socks, red socks, yellow socks, orange...

In a sock drawer, you have a pair of blue socks, red socks, yellow socks, orange socks, purple socks and green socks. You randomly pull out a sock one at a time until you select a pair of matching socks.

Let pr be the probability that you get your first matching pair on the r’th sock pulled from the drawer.

Find pr for r = 2, 3, . . ..
Math   Statistics-And-Probability   
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Answer #1

There are 6 pairs. Hence if more than 6 times socks are drawn (one at a time) then we must get matching pair.

Hence we are to find pr for r=2,3,4,5,6

In case of r draws, we have got one sock for each of r-1 different colour and in the last trial we have got the other piece of sock of any one of the chosen r-1 colour.

.

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