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Difficulty:
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Question Stats:
73% (01:28) correct
27%
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wrong
based on 52
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In a packet of M&M chocolates, there are only two colored M&M chocolates i.e. Green and Red. If two chocolates are picked randomly, then what is the probability of picking two red M&M chocolates?
(1) The probability of the first M&M chocolate being Green is 1/3.
(2) There are 48 red M&M chocolates in the packet.
(1) The probability of the first M&M chocolate being Green is 1/3.
(2) There are 48 red M&M chocolates in the packet.
28 Feb 2026, 02:02
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In a packet of M&M chocolates, there are only two colored M&M chocolates i.e. Green and Red. If two chocolates are picked randomly, then what is the probability of picking two red M&M chocolates?
(1) The probability of the first M&M chocolate being Green is 1/3.
(2) There are 48 red M&M chocolates in the packet.
We need to find out the probability of picking 2 red M&M chocolates. Let's look at each statement individually and then at both of them together (if required):
Statement 1: The probability of the first M&M chocolate being Green is 1/3.
Since there are only red and green chocolates, P(Red) = 2/3
Thus, ratio of red chocolates to the total number of chocolates = 2/3
However, we do not know the total number of chocolates, thus, there can be different probabilities associated.
Hence, Statement 1 is insufficient alone.
Now, let's take a look at Statement 2 closely:
Statement 2: There are 48 red M&M chocolates in the packet.
Even though we are given the number of red chocolates in the packet, we do not know the total number of chocolates in the packet.
Hence, Statement 2 is insufficient alone as well.
Now, let's take a look at the combination of both statements - Statement 1 and Statement 2:
Red = 2/3 of total
Red = 48
Now, total is fixed: Total = 3/2 * 48 = 72=> Probability is fixed.
P(Two Reds) = 48/72 * 47/71
Hence, the correct answer is Option C - BOTH statements (1) and (2) TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
Hope this helps!
(1) The probability of the first M&M chocolate being Green is 1/3.
(2) There are 48 red M&M chocolates in the packet.
We need to find out the probability of picking 2 red M&M chocolates. Let's look at each statement individually and then at both of them together (if required):
Statement 1: The probability of the first M&M chocolate being Green is 1/3.
Since there are only red and green chocolates, P(Red) = 2/3
Thus, ratio of red chocolates to the total number of chocolates = 2/3
However, we do not know the total number of chocolates, thus, there can be different probabilities associated.
Hence, Statement 1 is insufficient alone.
Now, let's take a look at Statement 2 closely:
Statement 2: There are 48 red M&M chocolates in the packet.
Even though we are given the number of red chocolates in the packet, we do not know the total number of chocolates in the packet.
Hence, Statement 2 is insufficient alone as well.
Now, let's take a look at the combination of both statements - Statement 1 and Statement 2:
Red = 2/3 of total
Red = 48
Now, total is fixed: Total = 3/2 * 48 = 72=> Probability is fixed.
P(Two Reds) = 48/72 * 47/71
Hence, the correct answer is Option C - BOTH statements (1) and (2) TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
Hope this helps!
28 Feb 2026, 05:29
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This is a classic Data Sufficiency probability question testing whether you understand the difference between knowing a ratio and knowing an actual count — and why both matter for dependent events.
What we need to find: P(both picks are red) = (R/T) x ((R-1)/(T-1)), where R = number of red chocolates and T = total chocolates.
Step 1 — Evaluate Statement 1 alone
P(first pick is Green) = 1/3, so P(first pick is Red) = 2/3.
This tells us R/T = 2/3 — red chocolates are 2/3 of the total.
But we don't know T. Could be 6 reds out of 9, or 48 reds out of 72, or 12 out of 18...
Different totals give different answers for P(two reds). Insufficient.
Step 2 — Evaluate Statement 2 alone
There are 48 red M&M chocolates, so R = 48.
But we have no idea what T is — we don't know the total number of chocolates.
Without the ratio of red to total, we can't compute the probability. Insufficient.
Step 3 — Combine both statements
From Statement 1: R/T = 2/3, which means T = (3/2) x R
From Statement 2: R = 48
So T = (3/2) x 48 = 72.
Now: P(two reds) = (48/72) x (47/71) — one unique, definite value. Sufficient.
Answer: C
The trap most people fall into: they see "P(Red) = 2/3" in Statement 1 and think "I know the probability of picking red, so I can calculate P(two reds)." You can't — not without replacement. Knowing the proportion is not enough; you need R and T as actual integers to plug into the without-replacement formula.
Takeaway: In Data Sufficiency probability questions involving sampling without replacement, a ratio alone is never sufficient — you always need at least one absolute count to anchor the calculation.
— Kavya | 725 (GMAT Focus) | Founder @ edskore.com
What we need to find: P(both picks are red) = (R/T) x ((R-1)/(T-1)), where R = number of red chocolates and T = total chocolates.
Step 1 — Evaluate Statement 1 alone
P(first pick is Green) = 1/3, so P(first pick is Red) = 2/3.
This tells us R/T = 2/3 — red chocolates are 2/3 of the total.
But we don't know T. Could be 6 reds out of 9, or 48 reds out of 72, or 12 out of 18...
Different totals give different answers for P(two reds). Insufficient.
Step 2 — Evaluate Statement 2 alone
There are 48 red M&M chocolates, so R = 48.
But we have no idea what T is — we don't know the total number of chocolates.
Without the ratio of red to total, we can't compute the probability. Insufficient.
Step 3 — Combine both statements
From Statement 1: R/T = 2/3, which means T = (3/2) x R
From Statement 2: R = 48
So T = (3/2) x 48 = 72.
Now: P(two reds) = (48/72) x (47/71) — one unique, definite value. Sufficient.
Answer: C
The trap most people fall into: they see "P(Red) = 2/3" in Statement 1 and think "I know the probability of picking red, so I can calculate P(two reds)." You can't — not without replacement. Knowing the proportion is not enough; you need R and T as actual integers to plug into the without-replacement formula.
Takeaway: In Data Sufficiency probability questions involving sampling without replacement, a ratio alone is never sufficient — you always need at least one absolute count to anchor the calculation.
— Kavya | 725 (GMAT Focus) | Founder @ edskore.com
