Tate has bag of golf balls: 3 red, 5 blue, 2 yellow, and 2 green. What is the probability that he pulls out a red one, replaces it, and then pulls out another red one?
1/16
To find the probability that Tate pulls out a red golf ball, replaces it, and then pulls out another red one, we can use the concept of independent events.
First, let's determine the probability of pulling out a red golf ball in one try.
Tate has a total of 3 red golf balls out of 3 + 5 + 2 + 2 = 12 golf balls. Therefore, the probability of pulling out a red golf ball on the first try is 3/12, which simplifies to 1/4.
Since we replace the ball after the first try, the total number of golf balls remains the same, and the probability of pulling out a red golf ball on the second try is also 1/4.
To find the probability of both events happening, we multiply their probabilities together since they are independent events.
Probability of pulling out a red golf ball on the first try = 1/4
Probability of pulling out a red golf ball on the second try = 1/4
Probability of both events happening = Probability of the first event × Probability of the second event
= (1/4) × (1/4)
= 1/16
Therefore, the probability that Tate pulls out a red golf ball, replaces it, and then pulls out another red one is 1/16.