An almirah stores 5 black and 4 white socks well mixed. A boy pulls out 2 socks at random. The probability that 2 are of the same colour is

Options

A. `4//9`
B. `5//8`
C. `5//9`
D. `7//12`

Answer

To solve the problem, we need to find the probability that two socks drawn at random from an almirah containing 5 black and 4 white socks are of the same color.

### Step-by-Step Solution:

1. **Identify Total Socks**:
- There are 5 black socks and 4 white socks.
- Total number of socks = 5 (black) + 4 (white) = 9 socks.

2. **Calculate Probability of Drawing Two Black Socks**:
- Probability of the first sock being black = Number of black socks / Total socks = 5/9.
- After drawing one black sock, there are now 4 black socks left and a total of 8 socks remaining.
- Probability of the second sock being black = Number of remaining black socks / Total remaining socks = 4/8 = 1/2.
- Therefore, the probability of both socks being black:
\[ P(\text{both black}) = P(\text{1st black}) \times P(\text{2nd black}) = \frac{5}{9} \times \frac{4}{8} = \frac{5}{9} \times \frac{1}{2} = \frac{5}{18}. \]

3. **Calculate Probability of Drawing Two White Socks**:
- Probability of the first sock being white = Number of white socks / Total socks = 4/9.
- After drawing one white sock, there are now 3 white socks left and a total of 8 socks remaining.
- Probability of the second sock being white = Number of remaining white socks / Total remaining socks = 3/8.
- Therefore, the probability of both socks being white:
\[ P(\text{both white}) = P(\text{1st white}) \times P(\text{2nd white}) = \frac{4}{9} \times \frac{3}{8} = \frac{4}{9} \times \frac{3}{8} = \frac{12}{72} = \frac{1}{6} = \frac{3}{18}. \]

4. **Calculate Total Probability of Drawing Two Socks of the Same Color**:
- Total probability of both socks being of the same color (either both black or both white):
\[ P(\text{same color}) = P(\text{both black}) + P(\text{both white}) = \frac{5}{18} + \frac{3}{18} = \frac{8}{18} = \frac{4}{9}. \]

### Final Answer:
The probability that the two socks drawn are of the same color is \(\frac{4}{9}\).