Final answer:
The probability that both pairs of socks selected are white is 6/13 after reducing the fraction. None of the answer choices exactly match this, but option (c) is equivalent when reduced.
Step-by-step explanation:
The probability that both pairs selected from the drawer are white is calculated by first finding the probability of selecting a white pair and then, given the first was white, selecting another white pair. The initial probability is 9 out of 13, since there are 9 white pairs and 13 pairs in total. Once a white pair is removed, there remain 8 white pairs out of the remaining 12 total pairs. Therefore, the calculation is (9/13) × (8/12).
To simplify, (8/12) reduces to (2/3), making the calculation (9/13) × (2/3). To find the final answer, multiply the numerators together and the denominators together: 9 × 2 = 18 for the numerators, and 13 × 3 = 39 for the denominators. Therefore, the probability is 18/39, which can be further reduced to 6/13.
None of the options given (a) 9/13, (b) 81/169, (c) 18/26, (d) 27/52 match the reduced fraction 6/13, indicating a possible error in the options provided. Out of the given options, 18/26 is equivalent to 6/13 when reduced, so option (c) would be the correct answer if it's assuming non-reduced fraction options.