Question

A bag contains 8 red marbles, 7 blue marbles and 5 green marbles. If two marbles are drawn out of the bag, what is the exact probability that both marbles drawn will be red?

Answer 1

To find the probability that both marbles drawn will be red, we need to determine the total number of possible outcomes and the number of favorable outcomes.

Total number of marbles in the bag: 8 red + 7 blue + 5 green = 20 marbles

When the first marble is drawn, there are 20 marbles in the bag, and 8 of them are red. So, the probability of drawing a red marble on the first draw is 8/20.

After drawing the first marble, we have one less marble in the bag, and the number of red marbles decreases by 1. So, on the second draw, there are 19 marbles left in the bag, and 7 of them are red. Therefore, the probability of drawing a red marble on the second draw, given that the first marble was red, is 7/19.

To find the probability of both marbles being red, we need to multiply the probabilities of each individual draw:

Probability of drawing a red marble on the first draw = 8/20
Probability of drawing a red marble on the second draw, given the first marble was red = 7/19

Probability of both marbles drawn being red = (8/20) * (7/19)

Simplifying the expression, we get:

(8/20) * (7/19) = 56/380 = 14/95

Therefore, the exact probability that both marbles drawn will be red is 14/95.