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115 students choose to attend one of three after school activities: football, tennis or running. There are 54 boys. 
52 students choose football, of which 25 are girls. 
43 students choose tennis. 
10 girls choose running. 
A student is selected at random.
What is the probability this student chose running? 
Give your answer in its simplest form.

 Jun 13, 2021
 #1
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Let n(F) choose football, n(T) in tennis, n(R) in running, n(B) boys and n(G) girls

 

  • n(F∪T∪R) = 115
  • n(B) = 54    ⇒n(G) = 115 - 54 = 61
  • n(F) = 52    ⇒n(F∩G) = 25    so    n(F∩B) = 52 - 25 = 27
  • n(T) = 43
  • n(R∩G) = 10

No. of girls in tennis

              n(T∩G) = n(G) - [n(F∩G) + n(R∩G)] = 61 - (25 + 10) = 26

No. of boys in tennis

              n(T∩B) = n(T) - n(T∩G) =  43 - 26 = 17 

Remaining no. of boys in running

              n(R∩B) = n(B) - [n(F∩B) - n(T∩B)] = 54 - (27 + 17) = 10

 

⇒n(R) = n(R∩G) + n(R∩B) = 10 + 10 = 20

 

Probability of choosing running 

            \(P(R) = {20\over 115} = {4\over 23}=0.17\)

 Jun 14, 2021

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