A bag contains 4 white, 3 blue, and 5 red marbles.
Find the probability of choosing a blue marble, then a red marble if the marbles are not replaced.
A. five over forty-four
B. fifteen over thirty-five
C. two-thirds
D. one over fifteen .
First, we need to find the probability of choosing a blue marble on the first draw, which is 3/12 (since there are 12 marbles total and 3 of them are blue). Then, on the second draw, we have 11 marbles left, since we did not replace the first one. There are now only 5 red marbles left out of the 11, so the probability of choosing a red marble on the second draw is 5/11.
To find the probability of both events happening together (choosing a blue marble, then a red marble), we multiply the probabilities:
3/12 * 5/11 = 15/132
Simplifying this fraction, we get:
5/44
Therefore, the answer is A. five over forty-four.
To find the probability of choosing a blue marble, then a red marble without replacement, we need to first determine the total number of marbles and then calculate the probability of each event individually.
Total number of marbles in the bag = 4 white + 3 blue + 5 red = 12 marbles
First, let's calculate the probability of choosing a blue marble as the first event:
Probability of choosing a blue marble = number of blue marbles / total number of marbles = 3 / 12 = 1/4
Since we do not replace the marble, the total number of marbles decreases by 1. Now, we have 11 marbles left in the bag.
Next, let's calculate the probability of choosing a red marble as the second event:
Probability of choosing a red marble = number of red marbles / (total number of marbles - 1) = 5 / 11
Now, to find the probability of both events occurring, we multiply the probabilities together:
Probability of choosing a blue marble, then a red marble = Probability of choosing a blue marble * Probability of choosing a red marble
= 1/4 * 5/11
= 5/44
Therefore, the answer to the question is A. five over forty-four.