Answer :
To answer this question, we need to precise the situation:
1. We have:
• 2 Red Socks
,• 4 White Socks
,• 10 Blue Socks
We have a total of 2 + 4 + 10 = 16 socks.
In this case "we draw out a sock and then we return it, and draw a second sock." We have here a "with replacement" situation. We have independent events.
Then, the probability that the first sock is white is:
[tex]P(white)=\frac{4}{16}=\frac{1}{4}[/tex]Since we return this sock to the drawer, we have that the probability that the second sock is blue is:
[tex]P(\text{blue)}=\frac{10}{16}=\frac{5}{8}[/tex]Therefore, the probability of these two events is:
[tex]P(W\cap B)=P(W)\cdot P(B)=\frac{1}{4}\cdot\frac{5}{8}\Rightarrow P(W\cap B)=\frac{5}{32}[/tex]In summary, the probability that the first sock is white and the second sock is blue is 5/32