Question

a drawer contains 2 Red Socks, four white socks, and 10 blue socks. Without looking you draw out a sock return it, and draw out a second sock. What is the probability that the first sock is white in the second sock is blue? Write your answer in fraction form

Answer 1

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:

`P(white)=(4)/(16)=(1)/(4)`

Since we return this sock to the drawer, we have that the probability that the second sock is blue is:

`P(\text{blue)}=(10)/(16)=(5)/(8)`

Therefore, the probability of these two events is:

`P(W\cap B)=P(W)\cdot P(B)=(1)/(4)\cdot(5)/(8)\Rightarrow P(W\cap B)=(5)/(32)`

In summary, the probability that the first sock is white and the second sock is blue is 5/32