A bag contains different colored balls; 7 yellow, 3 red, and 6 green. I randomly select one ball, note its color, put it back in the bag, and select another ball. What is the probability that both balls I selected were green, P(GG)?

1 answer

To find the probability of selecting two green balls, we need to consider the probability of selecting a green ball on the first draw and then the probability of selecting a green ball on the second draw.

The probability of selecting a green ball on the first draw is 6/16 because there are 6 green balls out of a total of 16 balls.

Since we put the first green ball back in the bag, the probability of selecting a green ball on the second draw is also 6/16.

To find the probability of both events happening, we multiply the probabilities: (6/16) * (6/16) = 36/256.

Therefore, the probability of selecting two green balls is 36/256, which simplifies to 9/64.