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25 Apr 2025, 04:06
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
56% (02:14) correct
44%
(02:57)
wrong
based on 9
sessions
History
Date
Time
Result
Not Attempted Yet
A poll conducted at Wembley Stadium revealed that \(\frac{1}{6}\) of Messi fans are also fans of Mbappe, \(\frac{2}{5}\) of Mbappe fans are also fans of De Bruyne, and \(\frac{3}{4}\) of De Bruyne fans are also fans of Ronaldo. What is the probability that a random Messi fan at the stadium is also a fan of Ronaldo?
(1) There is not a single Mbappe fan who is not also a fan of Messi.
(2) For every Messi fan who is also a fan of Mbappe, there are 5 Messi fans who are also fans of De Bruyne.
(1) There is not a single Mbappe fan who is not also a fan of Messi.
(2) For every Messi fan who is also a fan of Mbappe, there are 5 Messi fans who are also fans of De Bruyne.
25 Apr 2025, 04:06
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Official Solution:
A poll conducted at Wembley Stadium revealed that \(\frac{1}{6}\) of Messi fans are also fans of Mbappe, \(\frac{2}{5}\) of Mbappe fans are also fans of De Bruyne, and \(\frac{3}{4}\) of De Bruyne fans are also fans of Ronaldo. What is the probability that a random Messi fan at the stadium is also a fan of Ronaldo?
The question may seem convoluted at first, and it’s tempting to assign variables. However, simple reasoning and logic work better for this question. We are essentially asked to find the fraction of Messi fans who are also Ronaldo fans.
We’re told:
• \(\frac{1}{6}\) of Messi fans are also fans of Mbappe
• \(\frac{2}{5}\) of Mbappe fans are also fans of De Bruyne
• \(\frac{3}{4}\) of De Bruyne fans are also fans of Ronaldo
Notice that Messi fans and Ronaldo fans are not directly linked. We know that \(\frac{3}{4}\) of De Bruyne fans are also fans of Ronaldo; however, we know nothing about those Ronaldo fans who are not fans of De Bruyne, and more importantly, we know nothing about how Ronaldo fans and Messi fans overlap.
(1) There is not a single Mbappe fan who is not also a fan of Messi.
This implies that the Mbappe fans group is entirely inside the Messi fan group. Still, it is not sufficient, because we cannot establish the link between Messi fans and Ronaldo fans.
(2) For every Messi fan who is also a fan of Mbappe, there are 5 Messi fans who are also fans of De Bruyne.
This implies that the overlap between Messi and De Bruyne fans is 5 times the overlap between Messi and Mbappe fans. Still, it is not sufficient, since we cannot establish the link between Messi fans and Ronaldo fans.
(1) + (2) Let's assume there are 30 Messi fans. From (1), we get that there are 5 Mbappe fans, all of whom are Messi fans. From (2), we get that there are 25 Messi fans who are also De Bruyne fans. Since \(\frac{2}{5}\) of Mbappe fans are also fans of De Bruyne, the 5 and 25 groups have an overlap of 2 fans inside the Messi group. So, we have:
However, we still do not know how large the De Bruyne fan group outside the Messi group is, how large the Ronaldo fan group outside the De Bruyne group is, and most importantly, how Messi fans and Ronaldo fans overlap. Not sufficient.
Answer: E
A poll conducted at Wembley Stadium revealed that \(\frac{1}{6}\) of Messi fans are also fans of Mbappe, \(\frac{2}{5}\) of Mbappe fans are also fans of De Bruyne, and \(\frac{3}{4}\) of De Bruyne fans are also fans of Ronaldo. What is the probability that a random Messi fan at the stadium is also a fan of Ronaldo?
The question may seem convoluted at first, and it’s tempting to assign variables. However, simple reasoning and logic work better for this question. We are essentially asked to find the fraction of Messi fans who are also Ronaldo fans.
We’re told:
• \(\frac{1}{6}\) of Messi fans are also fans of Mbappe
• \(\frac{2}{5}\) of Mbappe fans are also fans of De Bruyne
• \(\frac{3}{4}\) of De Bruyne fans are also fans of Ronaldo
Notice that Messi fans and Ronaldo fans are not directly linked. We know that \(\frac{3}{4}\) of De Bruyne fans are also fans of Ronaldo; however, we know nothing about those Ronaldo fans who are not fans of De Bruyne, and more importantly, we know nothing about how Ronaldo fans and Messi fans overlap.
(1) There is not a single Mbappe fan who is not also a fan of Messi.
This implies that the Mbappe fans group is entirely inside the Messi fan group. Still, it is not sufficient, because we cannot establish the link between Messi fans and Ronaldo fans.
(2) For every Messi fan who is also a fan of Mbappe, there are 5 Messi fans who are also fans of De Bruyne.
This implies that the overlap between Messi and De Bruyne fans is 5 times the overlap between Messi and Mbappe fans. Still, it is not sufficient, since we cannot establish the link between Messi fans and Ronaldo fans.
(1) + (2) Let's assume there are 30 Messi fans. From (1), we get that there are 5 Mbappe fans, all of whom are Messi fans. From (2), we get that there are 25 Messi fans who are also De Bruyne fans. Since \(\frac{2}{5}\) of Mbappe fans are also fans of De Bruyne, the 5 and 25 groups have an overlap of 2 fans inside the Messi group. So, we have:
However, we still do not know how large the De Bruyne fan group outside the Messi group is, how large the Ronaldo fan group outside the De Bruyne group is, and most importantly, how Messi fans and Ronaldo fans overlap. Not sufficient.
Answer: E
03 Dec 2025, 21:17
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This is a gem of a question! This is one of those questions where you either spend 4 minutes on it, then decide to mark C and move ahead, ruining the whole test or spend 1 minute, get the idea and mark E!
