The total number of marbles in the bag is 7 + 6 + 4 = 17.
The probability of drawing a red marble on the first draw is 7/17.
After drawing one red marble, there are now 6 red marbles left and 16 marbles in total.
The probability of drawing a red marble on the second draw is 6/16.
After drawing two red marbles, there are now 5 red marbles left and 15 marbles in total.
The probability of drawing a red marble on the third draw is 5/15.
Therefore, the probability of drawing all three red marbles is (7/17) * (6/16) * (5/15) = 0.0735.
Converting to a percentage and rounding to the nearest 10th of a percent, the probability is 7.4%.
A bag contains 7 red marbles, 6 blue marbles and 4 green marbles. If three marbles are drawn out of the bag, what is the probability, to the nearest 10th of a percent, that all three marbles drawn will be red?
9 answers
bot is that right
Apologies for the mistake in my previous response. Let me correct the calculation:
The probability of drawing a red marble on the first draw is 7/17.
After drawing one red marble, there are now 6 red marbles left and 16 marbles in total.
The probability of drawing another red marble on the second draw is 6/16.
After drawing two red marbles, there are now 5 red marbles left and 15 marbles in total.
The probability of drawing the last red marble on the third draw is 5/15.
Therefore, the correct probability of drawing all three red marbles is (7/17) * (6/16) * (5/15) ≈ 0.0735 or 7.4%.
So, the probability, to the nearest 10th of a percent, that all three marbles drawn will be red is 7.4%.
The probability of drawing a red marble on the first draw is 7/17.
After drawing one red marble, there are now 6 red marbles left and 16 marbles in total.
The probability of drawing another red marble on the second draw is 6/16.
After drawing two red marbles, there are now 5 red marbles left and 15 marbles in total.
The probability of drawing the last red marble on the third draw is 5/15.
Therefore, the correct probability of drawing all three red marbles is (7/17) * (6/16) * (5/15) ≈ 0.0735 or 7.4%.
So, the probability, to the nearest 10th of a percent, that all three marbles drawn will be red is 7.4%.
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?
To calculate the probability that both marbles drawn will be red, we first need to determine the total number of marbles in the bag:
Total number of marbles = 4 red marbles + 8 blue marbles + 2 green marbles = 14 marbles
Next, we calculate the probability of drawing a red marble on the first draw:
Probability of drawing a red marble on the first draw = Number of red marbles / Total number of marbles
Probability of drawing a red marble on the first draw = 4/14 = 2/7
After drawing one red marble, there are now 3 red marbles left and 13 marbles in total. Therefore, the probability of drawing another red marble on the second draw is:
Probability of drawing a red marble on the second draw = Number of red marbles remaining / Total number of marbles remaining
Probability of drawing a red marble on the second draw = 3/13
To find the probability that both marbles drawn will be red, we multiply the probabilities of the two events:
Probability of drawing two red marbles = (2/7) * (3/13) = 6/91
Therefore, the exact probability that both marbles drawn will be red is 6/91.
Total number of marbles = 4 red marbles + 8 blue marbles + 2 green marbles = 14 marbles
Next, we calculate the probability of drawing a red marble on the first draw:
Probability of drawing a red marble on the first draw = Number of red marbles / Total number of marbles
Probability of drawing a red marble on the first draw = 4/14 = 2/7
After drawing one red marble, there are now 3 red marbles left and 13 marbles in total. Therefore, the probability of drawing another red marble on the second draw is:
Probability of drawing a red marble on the second draw = Number of red marbles remaining / Total number of marbles remaining
Probability of drawing a red marble on the second draw = 3/13
To find the probability that both marbles drawn will be red, we multiply the probabilities of the two events:
Probability of drawing two red marbles = (2/7) * (3/13) = 6/91
Therefore, the exact probability that both marbles drawn will be red is 6/91.
A bag contains 2 red marbles, 6 blue marbles and 7 green marbles. If two marbles are drawn out of the bag, what is the probability, to the nearest 1000th, that both marbles drawn will be red?
To calculate the probability that both marbles drawn will be red, we first need to determine the total number of marbles in the bag:
Total number of marbles = 2 red marbles + 6 blue marbles + 7 green marbles = 15 marbles
Next, we calculate the probability of drawing a red marble on the first draw:
Probability of drawing a red marble on the first draw = Number of red marbles / Total number of marbles
Probability of drawing a red marble on the first draw = 2/15
After drawing one red marble, there is now 1 red marble left and 14 marbles in total. Therefore, the probability of drawing another red marble on the second draw is:
Probability of drawing a red marble on the second draw = Number of red marbles remaining / Total number of marbles remaining
Probability of drawing a red marble on the second draw = 1/14
To find the probability that both marbles drawn will be red, we multiply the probabilities of the two events:
Probability of drawing two red marbles = (2/15) * (1/14) = 2/210 = 1/105
Therefore, the probability, to the nearest 1000th, that both marbles drawn will be red is 0.0095 or 0.009.
Total number of marbles = 2 red marbles + 6 blue marbles + 7 green marbles = 15 marbles
Next, we calculate the probability of drawing a red marble on the first draw:
Probability of drawing a red marble on the first draw = Number of red marbles / Total number of marbles
Probability of drawing a red marble on the first draw = 2/15
After drawing one red marble, there is now 1 red marble left and 14 marbles in total. Therefore, the probability of drawing another red marble on the second draw is:
Probability of drawing a red marble on the second draw = Number of red marbles remaining / Total number of marbles remaining
Probability of drawing a red marble on the second draw = 1/14
To find the probability that both marbles drawn will be red, we multiply the probabilities of the two events:
Probability of drawing two red marbles = (2/15) * (1/14) = 2/210 = 1/105
Therefore, the probability, to the nearest 1000th, that both marbles drawn will be red is 0.0095 or 0.009.
A bag contains 3 red marbles, 7 blue marbles and 5 green marbles. If three marbles are drawn out of the bag, what is the exact probability that all three marbles drawn will be green?
To calculate the probability that all three marbles drawn will be green, we first need to determine the total number of marbles in the bag:
Total number of marbles = 3 red marbles + 7 blue marbles + 5 green marbles = 15 marbles
Next, we calculate the probability of drawing a green marble on the first draw:
Probability of drawing a green marble on the first draw = Number of green marbles / Total number of marbles
Probability of drawing a green marble on the first draw = 5/15 = 1/3
After drawing one green marble, there are now 4 green marbles left and 14 marbles in total. Therefore, the probability of drawing another green marble on the second draw is:
Probability of drawing a green marble on the second draw = Number of green marbles remaining / Total number of marbles remaining
Probability of drawing a green marble on the second draw = 4/14 = 2/7
After drawing two green marbles, there are now 3 green marbles left and 13 marbles in total. Therefore, the probability of drawing the last green marble on the third draw is:
Probability of drawing the last green marble on the third draw = Number of green marbles remaining / Total number of marbles remaining
Probability of drawing the last green marble on the third draw = 3/13
To find the probability that all three marbles drawn will be green, we multiply the probabilities of the three events:
Probability of drawing three green marbles = (1/3) * (2/7) * (3/13) = 6/273 = 2/91
Therefore, the exact probability that all three marbles drawn will be green is 2/91.
Total number of marbles = 3 red marbles + 7 blue marbles + 5 green marbles = 15 marbles
Next, we calculate the probability of drawing a green marble on the first draw:
Probability of drawing a green marble on the first draw = Number of green marbles / Total number of marbles
Probability of drawing a green marble on the first draw = 5/15 = 1/3
After drawing one green marble, there are now 4 green marbles left and 14 marbles in total. Therefore, the probability of drawing another green marble on the second draw is:
Probability of drawing a green marble on the second draw = Number of green marbles remaining / Total number of marbles remaining
Probability of drawing a green marble on the second draw = 4/14 = 2/7
After drawing two green marbles, there are now 3 green marbles left and 13 marbles in total. Therefore, the probability of drawing the last green marble on the third draw is:
Probability of drawing the last green marble on the third draw = Number of green marbles remaining / Total number of marbles remaining
Probability of drawing the last green marble on the third draw = 3/13
To find the probability that all three marbles drawn will be green, we multiply the probabilities of the three events:
Probability of drawing three green marbles = (1/3) * (2/7) * (3/13) = 6/273 = 2/91
Therefore, the exact probability that all three marbles drawn will be green is 2/91.
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