Pat has five matched pairs of socks and no two of the pairs are the same color. If Pat selects two socks simultaneously and at random, what is the probability that the two socks selected will be a matched pair?

Rationale

The probability that the two socks selected will be a matched pair is {1/10}.

In this scenario, Pat has a total of 10 socks (5 matched pairs). When selecting 2 socks, there are 10 choose 2 (or 45) possible combinations, and only 5 of those combinations are matched pairs. Therefore, the probability of selecting a matched pair is 5 out of 45, which simplifies to {1/10}.

A ({1/2}) YOUR ANSWER

This choice suggests that half of the possible pairs of socks selected will be matched pairs. However, with 10 socks, there are 45 total combinations when selecting 2 socks, making it impossible for half of them to be matched pairs. Thus, this option is incorrect.

B ({1/4}) YOUR ANSWER

Choosing {1/4} implies that 25% of the combinations will be matched pairs. Given that there are only 5 matched combinations out of 45 total combinations, this fraction is not accurate. Therefore, this choice does not reflect the actual probability.

C ({1/5}) YOUR ANSWER

This choice indicates that 20% of the combinations would be matched pairs. Since there are 5 matched pairs and 45 total combinations, {1/5} overestimates the likelihood of selecting a matched pair. Thus, it is incorrect.

D ({1/9}) CORRECT

This option implies that the probability of selecting a matched pair is slightly higher than what the calculations support. Since only 5 out of 45 combinations yield matched pairs, this fraction does not represent the accurate probability, making it incorrect.

Conclusion

The probability of selecting a matched pair of socks from Pat's collection is calculated to be {1/10}, based on the total combinations possible and the number of matched pairs available. The other choices fail to accurately reflect the probability derived from the number of possible selections, reinforcing the importance of careful calculation in probability assessments.

Pat has five matched pairs of socks and no two of the pairs are the same color. If Pat selects two socks simultaneously and at random, what is the probability that the two socks selected will be a matched pair?

The probability that the two socks selected will be a matched pair is {1/10}.

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