Problem Solving

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

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?

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

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!!!

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