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?
A)
1/24
B)
1/22
C)
1/16
D)
5/12
Its Answer:
3\12 × 3\12 = 1\16
3 reds, 12 total
So, P(red,red) = 1/4 * 1/4
To find the probability that Tate pulls out a red golf ball, replaces it, and then pulls out another red ball, we need to know the total number of balls and the number of red balls.
Given that Tate has a bag with a total of 3 + 5 + 2 + 2 = 12 golf balls, and specifically 3 red balls, we can calculate the probability.
The probability of an event happening is calculated by taking the number of favorable outcomes (i.e., the desired outcome) and dividing it by the number of possible outcomes.
In this case, the desired outcome is pulling out a red ball, replacing it, and pulling out another red ball. Since the two events are independent, the probability of pulling out a red ball in each event is the same.
The probability of pulling out a red ball in one event is 3 (the number of red balls) divided by 12 (the total number of balls). This simplifies to 1/4.
Since these events are independent, we can multiply the probabilities together:
P(red and red) = P(red) × P(red) = (1/4) × (1/4) = 1/16
Therefore, the correct answer is C) 1/16.