If 40% of the students of a class like football, 75% of the students like basketball, and 30% like b

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04 Mar 2022 Probability

If 40% of the students of a class like football, 75% of the students like basketball, and 30% like both. If a student is picked at random who likes at least one of these games, what is the probability that he likes only football?

OPtion

1) 15/17
2) 2/13
3) 4/13
4) 9/17
5) 9/13
6) 8/13
7) 3/17
8) 8/17
9) 2/17
10) None of these

Solution

% of students who likes only football=40-30=10
% of students who likes at least one game=40+75-30=85
Required probability = P(Students likes only football) / P(Students who likes at least 1 game) = 10/85 = 2/17

Correct Option: 9 Best Solution (2)

Mayank Kandoi   2 years AGO

Let total students be x
Football = 40
Basketball = 75
Both games = 30

Hence,
Only football = 40-30 = 10
Only basketball = 75 - 30 = 45

Favourable outcomes = Only football = 10
Total sample space = 45+30+10 = 85 (since it is given that the picked child likes atleast one game)

Probability = 10/85 = 2/17
Option 9

Like? Yes (5) | No (1)  

Pargat Pal Singh   2 years AGO

As per given statement, 10% (40-30) like football only, 45% (75-30) like basketball only and 30% like both.
15% don't like any game.
Hence 85% like atleast one game.
Probability that randomly picked student (out of students who like at least one game) likes football only =10/85=2/17

Like? Yes (5) | No (2)