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In a class, 60% of students play soccer or basketball. If 10% play bot

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Bunuel
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In a class, 60% of students play soccer or basketball. If 10% play bot [#permalink] New post   21 Sep 2020, 04:00
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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 soccer only?

A. 0.1
B. 0.2
C. 0.3
D. 0.4
E. 0.5
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C
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Re: In a class, 60% of students play soccer or basketball. If 10% play bot [#permalink] New post   21 Sep 2020, 05:41
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Let Total no. of students = 100

the probability that a student chosen at random from the class plays basketball only = Students playing only Soccer/ total no. of students = 30/100 = 0.3

Answer is C
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Re: In a class, 60% of students play soccer or basketball. If 10% play bot [#permalink] New post   28 Sep 2020, 11:59
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Hi Yashika,
can you please explain how you got the split between non soccer as 20 and 40.
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Re: In a class, 60% of students play soccer or basketball. If 10% play bot [#permalink] New post   28 Sep 2020, 12:14
Pranithare wrote:
Hi Yashika,
can you please explain how you got the split between non soccer as 20 and 40.

See total is 100 (I let that total is 100)
so, if In a class, 60% of students play soccer or basketball.
60% of 100 = 60 play game, rest 40 are lazy (like me :lol: ) -------------------------(1)

If 10% play both sports => 10 people play both game ----------------------------(2)

and 60% do not play soccer= 60 do not play soccer ------------------(3)
=> so 40 does play soccer, with or without basketball ---------------------(4)

Put all 4 in Matrix, you will get value.
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Re: In a class, 60% of students play soccer or basketball. If 10% play bot [#permalink] New post   28 Sep 2020, 19:43
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Let there be a total of 100 players.

From Set Theory, Total = P(A U B) + P(A U B)' = Only A + Only B + P(A ∩ B) + P(A U B)' ... Equation (1)

Given P(A ∩ B) = 10% of 100 = 10

Also given that those who don't play soccer = Thse play only Hockey + P(S U H)' = 60% of 100 = 60

Putting these values in Equation (1), we get 100 = Only Soccer + 10 + 60

Those who play only soccer = 100 - 70 = 30


\(Probability = \frac{Favorable \space Outcomes}{Total \space Outcomes}= \frac{30}{100} = 0.3\)



Option C

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Re: In a class, 60% of students play soccer or basketball. If 10% play bot [#permalink] New post   30 Sep 2020, 22:25
Thanks Yashika, i missed that point even after drawing the matrix.
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Re: In a class, 60% of students play soccer or basketball. If 10% play bot [#permalink] New post   30 Sep 2020, 23:22
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Given


    • In a class, 60% of students play soccer or basketball.
    • 10% play both sports.
    • 60% do not play soccer.

To Find

    • The probability that a student chosen at random from the class plays soccer only.


Approach and Working Out

    • Let us assume, people who play only soccer is A%, only basketball = B%, both the sports = C% and none of the sports = D%
      o A + B +C + D = 100%

    • 60% of students play soccer or basketball.
      o A + B + C = 60%
      o D = 100 – 60 = 40%

    • 10% play both sports,
      o C = 10%
      o A + B = 100 – C – D
      o A + B = 50%

    • 60% do not play soccer.
      o B + D = 60%
      o B = 60 – D
      o B = 20%
      o A = 30%


    • Player who plays soccer only is A which is 30% and that will be the probability as well.

Correct Answer: Option C
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Re: In a class, 60% of students play soccer or basketball. If 10% play bot [#permalink] New post   01 Oct 2020, 03:03
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From Set Theory, Total = P(A U B) + P(A U B)' = Only A + Only B + P(A ∩ B) + P(A U B)'

Let the total number of players be 100.

=> 10% play both sports = P(A ∩ B) = \(\frac{10}{100}\) * 100 = 10

=> 60% do not play soccer = Only basketball + P(A U B)' = \(\frac{60}{100}\) * 100 = 60

=> 100 = Only soccer + 10 + 60

=> Only soccer = 30

=> Probability: \(\frac{30 }{ 100}\) = 0.3

Answer C
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In a class, 60% of students play soccer or basketball. If 10% play bot [#permalink] New post   01 Mar 2021, 21:18
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If 0.6 from the class do not play soccer, 0.4 do play soccer.

0.1 play both soccer and basketball.

0.4 - 0.1 = 0.3

0.3 is the probability that a student selected at random from the class plays soccer only.
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Re: In a class, 60% of students play soccer or basketball. If 10% play bot [#permalink] New post   12 Dec 2023, 04:26
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Re: In a class, 60% of students play soccer or basketball. If 10% play bot [#permalink]
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