The probability of picking a white sock and then a black sock from the drawer, with replacement, is 24/169 after reducing the fraction 96/676.
To find the probability of picking a white sock and then a black sock from a drawer with 12 white socks, 8 black socks, and 6 gray socks, we use the formula for independent events. The total number of socks is 12 + 8 + 6 = 26.
The probability of picking a white sock first is P(White) = ½12⁄26. After replacing the white sock, the probability of picking a black sock is P(Black) = ½8⁄26. Since the events are independent, you multiply the individual probabilities:
½P(White then Black) = P(White) × P(Black) = ½12⁄26 × ½8⁄26 = ½96⁄676.
Reducing the fraction 96/676, we get ½24⁄169 as the reduced fraction for the probability.