A probability problem by Ninad Pawar
Probability
Level
2
In a hostel , 25 students take tea, 20 students take coffee,15 students take milk,10 students take both tea and coffee, 8 students take both milk and coffee. None of them takes tea and milk both and everyone takes atleast one bevarage , find the number of students in the hostel.
The answer is 42.
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1 solution
We are given:
All people who took tea: 25
All people who took coffee: 20
All people who took milk: 15
All people who took BOTH tea and milk ONLY: 0
All people who took BOTH coffee and tea ONLY: 10
All people who took BOTH coffee and milk ONLY: 8
No one took all 3 beverages since no one took both tea and milk .
Take T as tea, C as coffee, M is milk, CT as coffee and tea, CM as coffee and milk. (Note that each student has to belong into one of these five categories)
ONLY T= ALL T - CT = 25- 10 = 15
ONLY C= ALL C - CT - CM =20 - 10 - 8 = 2
ONLY M= ALL M - CM = 15 - 8 = 7
All students
= ONLY T + ONLY C + ONLY M + CT + CM
= 15 + 2 + 7 + 10 + 8
= 42 (Answer)
Note: This can be solved with venn diagrams. (Unfortunately they confused me so much; I had to use other ways)