Two marbles are drawn from a bag containing 6 white, 4 red, and 6 green marbles. Find the probability of both marbles being white.
The probability of one of the marbles being white is 6/16=3/8 so the probability of both of the marbles being white is (3/8) x (3/8)
Jen's answer assumes that the first marble drawn is then returned to the bag.
If we simply draw two marbles, one after the other, the prob of the stated event is
6/16*5/15
= 1/8
To find the probability of both marbles being white, we need to know the total number of marbles and the number of white marbles in the bag.
In this case, there are 6 white marbles out of a total of 6 white + 4 red + 6 green = 16 marbles.
To find the probability of drawing a white marble on the first draw, we divide the number of favorable outcomes (white marbles) by the total number of outcomes (total marbles):
P(white on 1st draw) = 6/16 = 3/8.
After 1 white marble has been drawn, there are 5 white marbles left out of a total of 15 marbles (as one marble has been already removed).
To find the probability of drawing a white marble on the second draw, we divide the number of favorable outcomes (white marbles remaining) by the total number of outcomes (total marbles remaining):
P(white on 2nd draw) = 5/15 = 1/3.
To find the probability of both events happening (both marbles being white), we need to multiply the probabilities of each event occurring:
P(both marbles white) = P(white on 1st draw) × P(white on 2nd draw)
= (3/8) × (1/3)
= 3/24
= 1/8.
Therefore, the probability of drawing both marbles as white is 1/8.