How many will attend both?

Probability Level 1

A recent survey asked high school students whether or not they planned to go to the upcoming basketball game or the upcoming football game.

  • 200 total students were surveyed.

  • 58 students stated that they would miss at least one of the games (this includes the students that plan to miss both games).

How many students plan to attend both games?


The answer is 142.

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Andy Hayes by Andy Hayes , 38, USA

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4 solutions

Andy Hayes
Sep 7, 2016

"58 students would miss at least one of the games" can be interpreted as "58 students will miss the basketball game or miss the football game." By De Morgan's Laws , this set of 58 students is the complement of the set of students who will attend both games.

Therefore, the number of students who will attend both games is 200 − 58 = 142 200-58=\boxed{142} .

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Was the third point "None of the students r" meant to be deleted or was it just not completed?

Brian Charlesworth - 4 years, 9 months ago

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I was thinking about adding a third line there. It's strange, though. I didn't save that edit, and it wasn't showing up for me a second ago.

Andy Hayes - 4 years, 9 months ago

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Huh. Well, it's gone now and the question is clear without any further information, anyway.

Brian Charlesworth - 4 years, 9 months ago

Since there are only two games, the only possibilities are participating in both the games or not participating in at least one of them. So the number of students who are participating both the games is complement to that of students who are not participating in at least one game. And that is 142.

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Katelynn Griego
Oct 9, 2019

if 58 students plan to miss one or both then the difference of 200 and 58 would be the number of students that plan to attend both.

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Mario Toruno
Apr 7, 2019

58 students is the all encompass regardless of how many game are missed, it is the fact that a game is missed making it part of the set who will miss gams(set B), while the student body is set compromised of the population surveyed(set A), if broken into a venn diagram the middle is body represented of students attending(the intersect)

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