A box contains 9 socks, of which 4 are red and 5 are blue. We draw two socks from the box.What is the probability that they are of the same colour?

To solve this problem, we need to calculate the probability of drawing two socks of the same color. This can happen in two ways: either both socks are red or both socks are blue.

1. Calculate the probability of both socks being red: The probability of drawing the first red sock is 4/9 (since there are 4 red socks out of a total of 9). After drawing one red sock, there are now 3 red socks left out of a total of 8 socks. So, the probability of drawing a second red sock is 3/8. Therefore, the probability of drawing two red socks is (4/9) * (3/8) = 1/6.

2. Calculate the probability of both socks being blue: The probability of drawing the first blue sock is 5/9 (since there are 5 blue socks out of a total of 9). After drawing one blue sock, there are now 4 blue socks left out of a total of 8 socks. So, the probability of drawing a second blue sock is 4/8 = 1/2. Therefore, the probability of drawing two blue socks is (5/9) * (1/2) = 5/18.

3. Add the two probabilities together: The total probability of drawing two socks of the same color is the sum of the probabilities of drawing two red socks and two blue socks. So, the total probability is 1/6 + 5/18 = 1/6 + 5/18 = 2/6 + 5/18 = 7/18.

So, the probability that two socks drawn from the box are of the same color is 7/18.