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Bunuel
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In a class, 60% of students play soccer or basketball. If 10% play bot 18 Apr 2022, 04:15
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In a class, 60% of students play soccer or basketball. If 10% play both sports and 60% do not play soccer, what is the probability that a student chosen at random from the class plays only one of the sports?

A. 0.2
B. 0.3
C. 0.4
D. 0.5
E. 0.6
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Dragongirl24
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In a class, 60% of students play soccer or basketball. If 10% play bot 28 Apr 2022, 11:25
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Bunuel
In a class, 60% of students play soccer or basketball. If 10% play both sports and 60% do not play soccer, what is the probability that a student chosen at random from the class plays only one of the sports?

A. 0.2
B. 0.3
C. 0.4
D. 0.5
E. 0.6


can someone explain this?
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In a class, 60% of students play soccer or basketball. If 10% play bot 28 Apr 2022, 20:46
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Assume X students in class


soccer or Basketball：0.6x
Both soccer & Basketball：0.1x

No soccer（means only basketball）：0.6*0.6x（notice：not 60% of all students，but 60% of 0.6x）
Play soccer：0.6x-0.36x=0.24x （the number includes 0.1x)

Therefore, only soccer: 0.24x-0.1x=0.14x

Only Soccer+Only Basketball = 0.36x+0.14x=0.5x The answer! Drawing a Venn diagram will help.

I hope my reasoning is clear:) Let me know if there is anything I can improve.
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In a class, 60% of students play soccer or basketball. If 10% play bot 28 Apr 2022, 21:26
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Suppose T be total students in class

(Given) 0.4 T do not play both games.

So, T - 0.4 T = O.6 T play either Basketball or Soccer or both.

Also. (Given) 0.1 T play both games.

Therefore , play either games (only one game ) : 0.6 T - 0.1 T = 0.5 T

hence, Desired Probability = 0.5 T / T = 0.5

Hope it helps.
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In a class, 60% of students play soccer or basketball. If 10% play bot 28 Apr 2022, 23:29
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Bunuel
In a class, 60% of students play soccer or basketball. If 10% play both sports and 60% do not play soccer, what is the probability that a student chosen at random from the class plays only one of the sports?

A. 0.2
B. 0.3
C. 0.4
D. 0.5
E. 0.6

Say the class has 100 students. 60 play soccer or basketball. 10 play both.
Attachment:
Screenshot 2022-04-29 at 11.54.38.png
Screenshot 2022-04-29 at 11.54.38.png [ 30.12 KiB | Viewed 1927 times ]
Then number of people lying in yellow, green or blue regions are 60. We know that 10 lie in the green region.
Then number of people lying in the yellow or blue regions are 50. They are the ones who play either only soccer or only basketball.

50% students play only sport hence probability that the chosen student plays only one of these sports is 0.5
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