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Kaplan premier--Honor & sports

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by prachich1987 » Tue Dec 21, 2010 11:17 am
At Vally High school, 115 students failed to make the honor roll.In all, 150 seniors graduated.Ten more seniors made the honor roll than the number who played varsity sport.If 10 graduating seniors both made the honor roll and played varsity sports,what is the probability that any given graduating senior neither made the honor nor played varsity sports?

1) 1/15
2) 1/3
3) 2/5
4) 2/3
5) 27/30
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by diebeatsthegmat » Tue Dec 21, 2010 12:56 pm
prachich1987 wrote:At Vally High school, 115 students failed to make the honor roll.In all, 150 seniors graduated.Ten more seniors made the honor roll than the number who played varsity sport.If 10 graduating seniors both made the honor roll and played varsity sports,what is the probability that any given graduating senior neither made the honor nor played varsity sports?

1) 1/15
2) 1/3
3) 2/5
4) 2/3
5) 27/30
i am not sure for the answer i found but is the answer D?
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by Tani » Tue Dec 21, 2010 1:13 pm
The question is unclear. It says 115 "students" failed to make the honor role and then goes on to talk about seniors. If you assume the 115 refers to seniors, then 35 seniors did not make the honor role. That means 25 played sports.

We now have 35 on the honor role + 25 playing sports - 10 who do both, for a net of 50 students.

That means 100 students made neither so, 100/150 does indeed make 2/3
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by prachich1987 » Tue Dec 21, 2010 8:23 pm
Tani Wolff - Kaplan wrote:The question is unclear. It says 115 "students" failed to make the honor role and then goes on to talk about seniors. If you assume the 115 refers to seniors, then 35 seniors did not make the honor role. That means 25 played sports.

We now have 35 on the honor role + 25 playing sports - 10 who do both, for a net of 50 students.

That means 100 students made neither so, 100/150 does indeed make 2/3
Yes the answer is 2/3.
But can somebody explain it in terms of venn diagram..Thanks!!!
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by beat_gmat_09 » Tue Dec 21, 2010 8:36 pm
Total students = 150
Honor failed = 115
Honor made = 150 - 115 = 35
Honor Made = 10 + Varsity , Varsity = 35 - 10 = 25
Both = 10
Total = H + V - Both + Neither
Neither = Total - H - V + Both
= 150 - 25 - 35 + 10
= 150 - 50
= 100

Probability = Neither/Total = 100/150 = 2/3
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