My uncle’s ritual for dressing each morning except Sunday includes a trip to the sock drawer, where he:
(1) picks out three socks at random, then
(2) wears any matching pair and returns the odd sock to the drawer or
(3) returns the three socks to the drawer if he has no matching pair and repeats steps (1) and (3) until he completes step (2).

The drawer starts with 16 socks each Monday morning (eight blue, six black, two brown) and ends up with four socks each Saturday evening.

(a) On which day of the week does he average the longest time to dress?
(b) On which day of the week is he least likely to get a pair from the first three socks chosen?

Source: manchi tutorials

If the probability of getting a pair is p, then the expected number of attempts is 1/p.   So, at first blush, I thought that (a) and (b) had the same answer, but after thinking for a few seconds I realized that it is not necessarily so.  

Edited on June 28, 2013, 3:30 pm

Posted by Steve Herman on 2013-06-28 13:25:51