A bag contains 6 white and 4 black balls. two balls are drawn at random. Find the probability that they are of the same color.

Sure, here is the step by step solution:

Step 1: Identify the total number of balls. We have 6 white balls and 4 black balls, so the total number of balls is 6 + 4 = 10.

Step 2: Calculate the probability of drawing two white balls. The probability of drawing the first white ball is 6/10. After drawing one white ball, we have 5 white balls left and 9 total balls left. So, the probability of drawing a second white ball is 5/9. Therefore, the probability of drawing two white balls is (6/10) * (5/9) = 1/3.

Step 3: Calculate the probability of drawing two black balls. The probability of drawing the first black ball is 4/10. After drawing one black ball, we have 3 black balls left and 9 total balls left. So, the probability of drawing a second black ball is 3/9 = 1/3. Therefore, the probability of drawing two black balls is (4/10) * (1/3) = 2/15.

Step 4: Add the two probabilities together. The probability of drawing two balls of the same color is the probability of drawing two white balls plus the probability of drawing two black balls. So, the final probability is 1/3 + 2/15 = 11/30.

So, the probability that two balls drawn at random are of the same color is 11/30.