Question

A painter has 12 tins of paint. Seven tins are red, and five tins are yellow. Two tins are chosen at random. Calculate the probability that both tins are the same color.

a) 1/22
b) 5/11
c) 7/33
d) 14/33

Answer 1

The probability that both tins are the same color is 14/33.

Step-by-step explanation:

To calculate the probability that both tins are the same color, we need to consider the total number of possible outcomes and the number of favorable outcomes. There are two cases to consider: both tins are red or both tins are yellow.

Case 1: Both tins are red. We have 7 red tins, so the probability of choosing a red tin for the first pick is 7/12. After one red tin is chosen, there are 6 red tins left, so the probability of choosing a second red tin is 6/11. Therefore, the probability of both tins being red is (7/12) * (6/11).

Case 2: Both tins are yellow. We have 5 yellow tins, so the probability of choosing a yellow tin for the first pick is 5/12. After one yellow tin is chosen, there are 4 yellow tins left, so the probability of choosing a second yellow tin is 4/11. Therefore, the probability of both tins being yellow is (5/12) * (4/11).

Now, we can calculate the total probability by adding the probabilities from both cases: (7/12) * (6/11) + (5/12) * (4/11) = 14/33.