A bag contains 12 red, 14 purple and 10 green marbles. Suppose you reach in and grab two marbles. Find the probability of choosing a red marble, replacing it, and then choosing a green marble.
Your second event is not affected at all by what happened in the first event, so
Prob = (12/36)(10/36) = ....
To find the probability of choosing a red marble, replacing it, and then choosing a green marble, we need to consider two events:
1. The probability of choosing a red marble on the first draw (with replacement).
2. The probability of choosing a green marble on the second draw (with replacement).
Let's break down each event and calculate the probabilities.
1. Probability of choosing a red marble on the first draw:
The bag contains a total of 12 red marbles, 14 purple marbles, and 10 green marbles, making a total of 12 + 14 + 10 = 36 marbles.
Since we are replacing the marbles after each draw, the probability of choosing a red marble on the first draw is simply the probability of selecting one of the 12 red marbles from the total of 36 marbles. Therefore, the probability is:
P(red on first draw) = 12/36 = 1/3
2. Probability of choosing a green marble on the second draw:
After replacing the first marble back into the bag, there are still 12 red marbles, 14 purple marbles, and 10 green marbles in the bag, so the total number of marbles remains at 36.
Now we need to find the probability of choosing a green marble from the remaining 36 marbles. Since there are 10 green marbles, the probability is:
P(green on second draw) = 10/36 = 5/18
To find the probability of both events happening together (choosing a red marble first and then a green marble), we multiply the probabilities:
P(choosing red and then green) = P(red on first draw) * P(green on second draw)
= (1/3) * (5/18)
= 5/54
Therefore, the probability of choosing a red marble, replacing it, and then choosing a green marble is 5/54.