Question

Destiny has a bag with 3 green, 4 red, and 5 blue marbles. Destiny will pick 2 marbles from the bag, one at a time without looking. She will not replace a marble before picking the next marble. What is the probability of Destiny picking a red marble, followed by a green marble?

A. 1/12
B. 1/11
C. 7/12
D. 1/2

Answer 1

The probability of Destiny picking a red marble followed by a green marble is 1/11. This is obtained by multiplying the probability of picking a red marble first (4/12) by the probability of picking a green marble second (3/11) considering that there is no replacement.

Step-by-step explanation:

To find the probability that Destiny picks a red marble followed by a green marble, we need to consider the sample space and the event of interest. Destiny has a total of 3 green, 4 red, and 5 blue marbles, making a total of 12 marbles. On the first draw, the probability of getting a red marble is 4 out of 12 (since there are 4 red marbles). After picking a red marble, she does not replace it. Hence, there are now 11 marbles left in the bag, including 3 green ones. So, the probability of then picking a green marble is 3 out of 11.

The total probability of both events occurring in sequence (picking a red then a green marble) is the product of their probabilities:

P(Red then Green) = P(Red on first draw) × P(Green on second draw given Red was first) = (4/12) × (3/11)

Simplify the fractions and multiply them:

P(Red then Green) = (1/3) × (3/11) = 1/11

Therefore, the probability of Destiny picking a red marble followed by a green marble is 1/11, which corresponds to option B.

Answer 2

There are 4+3+5=12 marbles in the bag.
Let’s find how many green and red balls are in the bag. 4+3=7
So that means the probability of picking a red marble followed by a green marble is 7/12 (C)