Mr A's selection is Perfect

Probability Level 3

In a horse race, there are 5 horses. Mr A selects 2 horses at random. If the probability that one of the Mr A's horses wins the race can be expressed as a b \frac{a}{b} , where a a and b b are coprime positive integers, find the value of a + b a+b .


The answer is 7.

Md Zuhair by Md Zuhair , 20, India

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1 solution

  • The total number of ways to select 2 horses out of 5, N = ( 5 2 ) = 5 × 4 2 = 10 \displaystyle N = {5 \choose 2} = \dfrac {5\times 4}2 = 10
  • The number of ways to select 2 horses including the winning horse out of 5, N w = ( 4 1 ) = 4 \displaystyle N_w = {4 \choose 1} = 4
  • The probability of one of Mr A's horses wins the race, P r = N w N = 4 10 = 2 5 Pr = \dfrac {N_w}N = \dfrac 4{10} = \dfrac 25

⟹ a + b = 2 + 5 = 7 \implies a+b = 2+5 = \boxed{7}

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