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Brums
3 months ago
15

Imagine that after washing 5 distinct pairs of socks, you discover that two socks are missing! of course, you would like to have

the largest number of complete pairs remaining (duh!) thus, you are left with 4 complete pairs in the best-case scenario and with 3 complete pairs in the worst case. assuming that the probability of disappearance for each of the 10 socks is the same, find:
Mathematics
1 answer:
Zina [12.3K]3 months ago
5 0
Part A:

Considering the best possible outcome

The ideal case occurs if the two missing socks are from the same pair.
Consequently, there are 4 complete pairs remaining.

To choose 2 from the total of 10 socks (5 pairs), the number of combinations is given by 10C2 = 45.

Choosing 2 that are from the same pair means selecting one from 5 pairs, so the count is 5C1 = 5.

Thus, the probability for this best case is 5 / 45 = 1 / 9.

Part B:

Considering the worst-case outcome

This scenario occurs when the two missing socks are from different pairs.
As a result, we have 3 complete pairs left.

The total ways to select 2 socks from 10, again, is 10C2 = 45.

To select 2 that do not belong to the same pair, we calculate as follows: 10C2 - 5C1 = 45 - 5 = 40.

Therefore, the probability for the worst-case scenario is 40 / 45 = 8 / 9.
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