A bag contains 4 red marbles, 8 blue marbles and 2 green marbles. If two marbles are drawn out of the bag, what is the exact probability that both marbles drawn will be red?
There are a total of 14 marbles in the bag. The probability of drawing a red marble on the first draw is 4/14. After one red marble is drawn, there are only 3 red marbles left in the bag out of a total of 13 marbles remaining. Therefore, the probability of drawing a red marble on the second draw, given that the first marble drawn was red, is 3/13.
To find the probability of both marbles drawn being red, we need to multiply the probability of drawing a red marble on the first draw by the probability of drawing a red marble on the second draw:
(4/14) x (3/13) = 12/182
Simplifying this fraction gives:
2/26
This can be simplified further by dividing both the numerator and denominator by 2:
1/13
Therefore, the exact probability of both marbles drawn being red is 1/13.