Question
A jar has 13 marbles and eight of them are green. You pull two marbles without replacement it. What is the probability that they both are green
Answers
GPT 3.5
To find the probability that both marbles are green, we first need to calculate the probability of pulling a green marble on the first draw and then a green marble on the second draw.
The probability of pulling a green marble on the first draw is the number of green marbles divided by the total number of marbles:
P(Green on first draw) = 8/13
Since we did not replace the first marble, there are now 12 marbles left, 7 of which are green. So the probability of pulling a green marble on the second draw, after pulling a green marble on the first draw, is:
P(Green on second draw) = 7/12
To find the combined probability of both events occurring, we simply multiply the individual probabilities:
P(Both green) = P(Green on first draw) * P(Green on second draw) = (8/13) * (7/12)
P(Both green) = 56 / 156 = 7 / 19
Therefore, the probability that both marbles drawn are green is 7/19.
The probability of pulling a green marble on the first draw is the number of green marbles divided by the total number of marbles:
P(Green on first draw) = 8/13
Since we did not replace the first marble, there are now 12 marbles left, 7 of which are green. So the probability of pulling a green marble on the second draw, after pulling a green marble on the first draw, is:
P(Green on second draw) = 7/12
To find the combined probability of both events occurring, we simply multiply the individual probabilities:
P(Both green) = P(Green on first draw) * P(Green on second draw) = (8/13) * (7/12)
P(Both green) = 56 / 156 = 7 / 19
Therefore, the probability that both marbles drawn are green is 7/19.