Answer:
To calculate the probability of drawing a white pair followed by a blue pair without replacement, you need to consider the probability of each step.
1. Probability of first drawing a white sock: 2 white socks out of a total of 10 socks (2 white + 5 blue + 3 brown).
\( P(\text{white}) = \frac{2}{10} \).
2. After drawing a white sock, the total number of socks is reduced to 9.
3. Probability of second drawing a white sock: Now there is 1 white sock left out of the remaining 9 socks.
\( P(\text{white again}) = \frac{1}{9} \).
4. Probability of third drawing a blue sock: There are 5 blue socks left out of the remaining 8 socks.
\( P(\text{blue}) = \frac{5}{8} \).
5. After drawing a blue sock, the total number of socks is reduced to 7.
6. Probability of fourth drawing a blue sock: Now there are 4 blue socks left out of the remaining 7 socks.
\( P(\text{blue again}) = \frac{4}{7} \).
To find the probability of the entire sequence (white pair followed by a blue pair), you multiply the individual probabilities:
\[ P(\text{white pair then blue pair}) = P(\text{white}) \times P(\text{white again}) \times P(\text{blue}) \times P(\text{blue again}) \]
\[ = \frac{2}{10} \times \frac{1}{9} \times \frac{5}{8} \times \frac{4}{7} \]
This simplifies to \( \frac{1}{84} \).
Therefore, none of the provided options (A. 2/5, B. 1/3, C. 1/9, D. 1/10) match the calculated probability. Please double-check the options or the problem statement.
