A bag contains 3 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 of marbles drawn will be red?
The probability of drawing a red marble on the first draw is 3/13 (since there are 3 red marbles out of 13 total marbles in the bag).
After the first red marble is drawn, there are only 2 red marbles left out of 12 total marbles remaining in the bag. Therefore, the probability of drawing a second red marble is 2/12, or 1/6.
To find the probability of both events happening (drawing a red marble on the first draw and a red marble on the second), we multiply the individual probabilities together:
(3/13) x (1/6) = 3/78
So the exact probability of drawing two red marbles out of the bag is 3/78, or approximately 0.0385.
A bag contains 7 red marbles, 8 blue marbles and 3 green marbles. If two marbles are drawn out of the bag, what is the exact probability that both marbles will be red?
The probability of drawing a red marble on the first draw is 7/18 (since there are 7 red marbles out of 18 total marbles in the bag).
After the first red marble is drawn, there are only 6 red marbles left out of 17 total marbles remaining in the bag. Therefore, the probability of drawing a second red marble is 6/17.
To find the probability of both events happening (drawing a red marble on the first draw and a red marble on the second), we multiply the individual probabilities together:
(7/18) x (6/17) = 42/306
We can simplify this fraction by dividing both the numerator and denominator by 6, which gives us:
7/51
So, the exact probability of drawing two red marbles out of the bag is 7/51.
A bag contains 6 red marbles, 5blue marbles, and 4 green marbles. If three marbles are drawn out of the bag, what is the exact probability that all three marbles drawn will be blue?
The probability of drawing a blue marble on the first draw is 5/15 (since there are 5 blue marbles out of 15 total marbles in the bag).
After the first blue marble is drawn, there are only 4 blue marbles left out of 14 total marbles remaining in the bag. Therefore, the probability of drawing a second blue marble is 4/14, or 2/7.
After the second blue marble is drawn, there are only 3 blue marbles left out of 13 total marbles remaining in the bag. Therefore, the probability of drawing a third blue marble is 3/13.
To find the probability of all three events happening (drawing a blue marble on each of the three draws), we multiply the individual probabilities together:
(5/15) x (4/14) x (3/13) = 6/455
So the exact probability of drawing three blue marbles out of the bag is 6/455.
That was wrong
I apologize for the mistake in my previous response. Here is the correct solution:
The probability of drawing a blue marble on the first draw is 5/15 (since there are 5 blue marbles out of 15 total marbles in the bag).
After the first blue marble is drawn, there are now only 4 blue marbles left out of 14 total marbles remaining in the bag. Therefore, the probability of drawing a second blue marble is 4/14, or 2/7.
After the second blue marble is drawn, there are now only 3 blue marbles left out of 13 total marbles remaining in the bag. Therefore, the probability of drawing a third blue marble is 3/13.
To find the probability of all three events happening (drawing a blue marble on each of the three draws), we multiply the individual probabilities together:
(5/15) x (4/14) x (3/13) = 2/455
So the exact probability of drawing three blue marbles out of the bag is 2/455.
It was 2/91
I apologize again for giving you incorrect answer. You are right, the correct probability of drawing three blue marbles out of the bag is 2/91. Here is the correct solution:
The probability of drawing a blue marble on the first draw is 5/15 (since there are 5 blue marbles out of 15 total marbles in the bag).
After the first blue marble is drawn, there are now only 4 blue marbles left out of 14 total marbles remaining in the bag. Therefore, the probability of drawing a second blue marble is 4/14, or 2/7.
After the second blue marble is drawn, there are now only 3 blue marbles left out of 13 total marbles remaining in the bag. Therefore, the probability of drawing a third blue marble is 3/13.
To find the probability of all three events happening (drawing a blue marble on each of the three draws), we multiply the individual probabilities together:
(5/15) x (2/7) x (3/13) = 2/91
So the exact probability of drawing three blue marbles out of the bag is 2/91.