Part A:
The probability on the best case scenario
The best case scenario results when the two missing socks are of the same pair.
Thus, there are 4 complete pairs of socks not missing.
Now, the number of ways of selecting 2 socks from a total of 5 x 2 = 10 socks is given by 10C2 = 45
The number of ways of selecting 2 socks from 10 sucks such that the two socks are of the same pair is the same as the probability of selecting 1 pair of socks from 5 pairs and is given by 5C1 = 5
Therefore, the probability of the best case scenario is given by 5 / 45 = 1 / 9
Part B:
The probability on the worst case scenario
The worst case scenario results when the two missing socks are not of the same pair.
Thus, there are 3 complete pairs of socks not missing.
Now, the number of ways of selecting 2 socks from a total of 5 x 2 = 10 socks is given by 10C2 = 45
The
number of ways of selecting 2 socks from 10 sucks such that the two
socks are not of the same pair is given by 10C2 - 5C1 = 45 - 5 = 40
Therefore, the probability of the worst case scenario is given by 40 / 45 = 8 / 9
