Mathematics Probability

Question

Tony had 5 red socks, 3 blue socks, and 2 white socks in a drawer. He pulled out 2 socks at random from the drawer. What is the probability that one sock is blue, and the other is red?

Answer 1

number of ways to pick one blue sock out of 3 = 3 C 1 = 3

number of ways to pick one red sock out of 5 = 5 C 1 = 5

number of ways to pick one blue sock and one red sock = 3 * 5 = 15

number of ways to pick 2 socks out of 10 = 10 C 2 = 45

probability = number of ways to pick one blue sock and one red sock / number of ways to pick 2 socks out of 10 = 15/45 = 1/3

another way:

probability pick blue sock then red sock = 3/10 * 5/9 = 1/6

probability pick red sock then blue sock = 5/10 * 3/9 = 1/6

probability pick red and blue sock in either order = 1/6 + 1/6 = 1/3

Answer 2

You can make a tree diagram like this:

You can see there are two ways to get a red and blue sock, both have a probability of 1/6. 1/6 + 1/6 = 2/6 = 1/3