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19 Dec 2024, 09:00
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12 Days of Christmas 2024 - 2025 Competition with $40,000 of Prizes
A jar contains only red, blue and green marbles. If 2 marbles are selected at random, one after the other, with replacement, what is the probability that the first marble is red and the second is green?
(1) The ratio of red marbles to the combined total of blue and green marbles is 1:2, and the ratio of blue marbles to the combined total of red and green marbles is 1:5.
(2) The jar contains 8 red marbles.
A jar contains only red, blue and green marbles. If 2 marbles are selected at random, one after the other, with replacement, what is the probability that the first marble is red and the second is green?
(1) The ratio of red marbles to the combined total of blue and green marbles is 1:2, and the ratio of blue marbles to the combined total of red and green marbles is 1:5.
(2) The jar contains 8 red marbles.
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19 Dec 2024, 10:00
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Bunuel
GMAT Club's Official Explanation:
A jar contains only red, blue and green marbles. If 2 marbles are selected at random, one after the other, with replacement, what is the probability that the first marble is red and the second is green?
First, note that the marbles are picked with replacement, meaning the first marble is returned to the jar after it is picked. This implies that knowing only the ratios of the marbles is sufficient to answer the question, as the initial ratio will not change after the first pick.
(1) The ratio of red marbles to the combined total of blue and green marbles is 1:2, and the ratio of blue marbles to the combined total of red and green marbles is 1:5.
This implies that
• red : (blue + green) = 1 : 2, thus red : total = 1 : (1 + 2) = 1 : 3. Therefore, 2 out of 6 marbles are red.
• blue : (red + green) = 1 : 5, thus blue : total = 1 : (1 + 5) = 1 : 6. Therefore, 1 out of 6 marbles is blue.
Now, if 2 out of 6 marbles are red and 1 out of 6 marbles is blue, the remaining 3 out of 6 marbles must be green. Thus, the probability of the first marble being red and the second being green is 2/6 * 3/6 = 1/6. Sufficient.
(2) The jar contains 8 red marbles.
Knowing only the number of red marbles is clearly not enough to answer the question. Not sufficient.
Answer: A.
General Discussion
19 Dec 2024, 09:28
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P(red)* P(green) = ?
Statement 2 : Total number of red marbles = 8
This statement is insufficient
Let r be red, b be blue and g be green then,
Statement 1 : r/(b + g) = 1/2 and b/(r + g) = 1/5
r/(b + g) = 1/2
r/(r + b + g) = 1/3 = 2/6
b/(r + g) = 1/5
b/(r + b + g) = 1/6
g/(r + b + g) = 1 - r/(r + b + g) - b/(r + b + g) = 1 - 2/6 - 1/6 = 1 - 3/6 = 3/6
P(red) = r/(r + b +g) = 2/6
P(green) = g/(r + b + g) = 3/6
P = P(red)*P(green)=(2/6)*(3/6)=1/6
This statement is sufficient.
Answer: A
Statement 2 : Total number of red marbles = 8
This statement is insufficient
Let r be red, b be blue and g be green then,
Statement 1 : r/(b + g) = 1/2 and b/(r + g) = 1/5
r/(b + g) = 1/2
r/(r + b + g) = 1/3 = 2/6
b/(r + g) = 1/5
b/(r + b + g) = 1/6
g/(r + b + g) = 1 - r/(r + b + g) - b/(r + b + g) = 1 - 2/6 - 1/6 = 1 - 3/6 = 3/6
P(red) = r/(r + b +g) = 2/6
P(green) = g/(r + b + g) = 3/6
P = P(red)*P(green)=(2/6)*(3/6)=1/6
This statement is sufficient.
Answer: A
