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Comment on Odd or Even
Say there are 5 matching
though not sure
Perfect!
Perfect!
P(no matching pair) = P(select ANY sock as 1st selection AND select a NON-MATCHING sock as 2nd selection)
= P(select ANY sock as 1st selection) x P(select a NON-MATCHING sock as 2nd selection)
= 1 x 8/9
= 8/9
ASIDE: For others following along, the second probability is 8/9, because once we've selected the 1st sock, there are 9 socks remaining. Of these 9 socks, 1 sock matches the 1st sock selected, and the other 8 socks are NOT a match.
Hi Brent,
If it were a counting question asking how many ways we can select two non matching sock, how would we go about it using FCP ?
Here's one approach:
Here's one approach:
First off, let's say that, for each pair of matching socks, we have a left sock and a right sock.
STAGE 1: Choose 2 colors
There are 5 colors. Since the order in which we select the socks does not matter, we can use combinations.
We can select 2 colors from 5 colors in 5C2 ways (10 ways)
ASIDE: Now, from each color, we'll select either a left sock or a right sock
STAGE 2: From one color, choose a left or right sock
This can be accomplished in 2 ways
STAGE 3: From the other color, choose a left or right sock
This can be accomplished in 2 ways
TOTAL number of ways to select 2 NON-MATCHING socks = (10)(2)(2)
= 40
For "fun", let's also determine the denominator.
TOTAL number of ways to select ANY 2 socks = 10C2 = 45
So, P(no matching pair) = 40/45 = 8/9
Cheers,
Brent