A box contains pair of socks of two colours (black and white). I have picked out a white socks. I pick out one more with my eyes closed. What is the probability that it will make a pair ?

Answer

To solve the problem step by step, we will determine the probability of picking a sock that will make a pair with the white sock already picked.

### Step 1: Identify the socks in the box
Let's assume the box contains:
- 2 white socks
- 2 black socks

### Step 2: Determine the sock already picked
You have already picked one white sock.

### Step 3: Identify the remaining socks
After picking one white sock, the remaining socks in the box are:
- 1 white sock (since you picked one)
- 2 black socks

### Step 4: Determine the favorable outcomes
To make a pair with the white sock you have already picked, you need to pick the remaining white sock. Therefore, there is only **1 favorable outcome** (picking the remaining white sock).

### Step 5: Determine the total outcomes
The total number of socks remaining in the box is:
- 1 white sock + 2 black socks = 3 socks

### Step 6: Calculate the probability
The probability of picking a sock that will make a pair with the white sock is given by the formula:

\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]

Substituting the values we found:
\[ \text{Probability} = \frac{1}{3} \]

### Final Answer
The probability that the second sock picked will make a pair with the first white sock is \(\frac{1}{3}\).

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