SOLUTION: you have 10 pairs of socks,five black and five blue,but they are not paired up.instead they are all mixed up in a drawer.it is early in the morning and you do not want to turn on t

Question 1054507: you have 10 pairs of socks,five black and five blue,but they are not paired up.instead they are all mixed up in a drawer.it is early in the morning and you do not want to turn on the light.
1. how many socks must you pull out to guarantee that you have a pair of one color?
2. how many must you pull out to have two good pairs(each pair is the same color)?
3. how many must you pull out to be certain that you have a pair of black socks? use a systematic approach to list all possible outcomes as a way to justify the answer in each case.
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
(1)
You want either 2 black socks or 2 blue socks
The WORST case for 2 picks is:
[ blk ] & [ blu ]
The 3rd pick guarantees you will have 1 pair
( either [ pair of blk ] or [ pair of blu ] )
------------------------------------------
(2)
You want either [ 2 pairs of blk ] or [ 2 pairs of blu ]
The WORST case for picks is:
[ blk ], [ blu ], [ blu ], [ blk ], [ blu ], [ blk ]
in any order, so
[ blk ], [ blk ], [ blk ], [ blu ], [ blu ], [ blu ]
So, you have made 6 picks and you still don't
have 2 pairs of the same color.
The 7th pick guarantees in this worst case
you will have 2 pairs of the same color
--------------------------------------------
(3)
You want 1 pair of black socks
The worst case is:
[ 5 blu ]
The 6th pick guarantees you will have 1 pair
of black socks
--------------------------------------------
Note that any other combination for the 1st 5 picks
except [ 5 blu ] will give you at least [ 2 blk ] socks

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