A bag contains 4 red marbles, 3 blue marbles, and 6 green marbles. If two marbles are drawn out of the bag, what is the probability, of the nearest 1000th, that both marbles will be red?
There are a total of 13 marbles in the bag. The probability of drawing a red marble on the first try is 4/13. After one red marble is drawn, there will be 3 red marbles left out of 12 total marbles. Therefore, the probability of drawing a second red marble is 3/12 (since one marble has already been drawn and removed).
To find the probability of both events happening (drawing two red marbles in a row), you multiply the probabilities together:
(4/13) x (3/12) = 1/13
So the probability of drawing two red marbles out of the bag is 1/13, or approximately 0.077 to the nearest 1000th.
To find the probability of drawing two red marbles, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total number of marbles = 4 red marbles + 3 blue marbles + 6 green marbles = 13 marbles.
The probability of drawing the first red marble is 4/13.
After removing one red marble, we have 3 red marbles left out of a total of 12 marbles.
Therefore, the probability of drawing the second red marble is 3/12.
To find the probability of both events occurring, we multiply the probabilities of each event:
P(First red marble) * P(Second red marble) = 4/13 * 3/12 = 12/156 = 1/13.
Thus, the probability, rounded to the nearest thousandth, that both marbles drawn will be red is 0.077.