33.
A bag of marbles contains 5 red, 3 blue, 2 green, and 2 yellow marbles.
What is the probability that you choose a red marble and then a green marble assuming you replace the first marble?
A) 1/24
B) 5/72
C) 5/66
D) 5/6
5/12 times 2/12 with replacement
5/72 is your anwser
To calculate the probability of choosing a red marble and then a green marble, assuming you replace the first marble, you need to find the individual probabilities of choosing a red marble and a green marble, and then multiply them together.
The probability of choosing a red marble is given by the ratio of the number of red marbles to the total number of marbles:
Probability of choosing a red marble = Number of red marbles / Total number of marbles
Probability of choosing a red marble = 5 / (5 + 3 + 2 + 2) = 5 / 12
Since the first marble is replaced, the number of marbles remains the same for the second draw. Therefore, the probability of choosing a green marble is also 2 / 12.
Now, to calculate the probability of both events happening, you multiply the probabilities together:
Probability of choosing a red marble and then a green marble = Probability of choosing a red marble * Probability of choosing a green marble
Probability of choosing a red marble and then a green marble = (5 / 12) * (2 / 12) = 10 / 144
Simplifying the fraction, we get:
Probability of choosing a red marble and then a green marble = 5 / 72
Therefore, the correct answer is B) 5/72.
To calculate the probability of choosing a red marble and then a green marble, assuming you replace the first marble, you need to consider two independent events: choosing a red marble and choosing a green marble.
First, let's find the probability of choosing a red marble.
The bag contains a total of 5 red marbles, so the probability of choosing a red marble on the first pick is 5/12 (since there are 12 marbles in total).
Next, since we are assuming that we replace the first marble, the probabilities of choosing a green marble are the same for both picks.
The bag contains 2 green marbles, so the probability of choosing a green marble on any pick is 2/12 (since there are still 12 marbles in total after replacing the first one).
To find the probability of both events happening (choosing a red marble and then a green marble), you multiply the probabilities of each event occurring.
So the probability of choosing a red marble and then a green marble is (5/12) * (2/12) = 10/144 = 5/72.
Therefore, the correct answer is B) 5/72.