Question 12

The probability that the two socks selected will be a matched pair is 1/9.

To determine the probability that the two socks selected will be a matched pair, we calculate the total ways to choose 2 socks from 10 and the ways to choose 2 matched socks from the 5 pairs. The probability is then the ratio of these two quantities, which results in 1/9.

A) 1/2

This option suggests that the probability of selecting a matched pair is 1/2. However, this is incorrect because there are multiple combinations of socks that can be selected, and the likelihood of selecting a matched pair is much lower than this value.

B) 1/4

Choosing a probability of 1/4 implies that out of every four selections, one would be a matched pair. This does not accurately reflect the total combinations available when drawing from 10 socks, making this option incorrect.

C) 1/5

The probability of 1/5 would indicate that one out of every five selections results in a matched pair. While closer than previous options, it still does not account for the total combinations and is therefore not the correct probability.

D) 1/9

This is the correct answer. The total number of ways to choose 2 socks from 10 is 45, and the number of ways to choose 2 socks from the same pair is 5. Thus, the probability of selecting a matched pair is 5/45, which simplifies to 1/9.

E) 1/10

This option suggests that the probability of selecting a matched pair is 1/10. It does not accurately represent the calculated probability, as it underestimates the combinations available when selecting from 10 socks.

Conclusion

The correct probability of selecting a matched pair of socks is definitively 1/9, as derived from the total combinations of sock selections. All other options inaccurately represent the likelihood based on the available pairs and total socks, leading to their incorrectness.