At a high school, 300 students are members of the band, chess club, or

Question

At a high school, 300 students are members of the band, chess club, or both. If 200 students are members of the band only and 50 students are members of the band and chess club, what is the probability that a student chosen at random is a member of only the chess club?

A. 1/6
B. 1/5
C. 1/4
D. 1/3
E. 1/2

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Sonatomar · Answer

"300 students are members of the band, chess club, or both"
means 300 is the entire group.
So we simply divide the group into:

200+50+50=300

Then probability = favorable ÷ total:

50/300=1/6
 ​
 ​

​

onlyPlanA · Answer

Total = Only Band + Only Chess + Both
300 = 200 + Only Chess + 50
Only Chess = 50

So, probability that only chess member will be selected = 50/300 = 1/6

Option A.

abhishekb1352 · Answer

Using the formula
Total = A only + B only + Both
Given, Band only = 200, Both = 50, then total = 300
300 = 200+50+Chess
Chess = 50

P(People who only play chess) = 50/300 = 1/6 
Answer is Option A

PS: Do not use the formula blindly, I initially thought of using the formula total = A + B - Both, which gave me wrong answer obviously, then I read the argument again with clarity in mind.

TheAdmissionHub · Answer

Let  B  be the members of the band,  C  the members of the chess club and  BC  the members of both of them.

Total:  T=300 
 
B-BC=200
BC=50
 
 T=B+C-BC  ⭢  300=C+200  ⭢  C=100

Members of only C:  C-BC = 100-50=50

Therefore, the probability is:  \frac{50}{300} = \frac{1}{6}

Answer: A

At a high school, 300 students are members of the band, chess club, or

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At a high school, 300 students are members of the band, chess club, or

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