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Five horses are in a race. Mr. A selects two of the horses at random and bets on them. The probability that Mr. A selected the winning horse is

Five horses are in a race. Mr. A selects two of the horses at random and bets on them. The probability that Mr. A selected the winning horse is

Grade:12th pass

1 Answers

Arun
25757 Points
4 years ago
Dear Pawan
 
 
In total there are 5 horses. out of these Mr A selects two horses. This can be done in \binom{5}{2}(5C2)=10 ways.
Out of the five horses only one horse wins. Let us say Mr A has selected the horse. He has to select one more horse so that his set of two has the winning horse. out of remaining 4 one can be selected in \binom{4}{1}ways.Thus 
n(E)=\binom{4}{1}=4
n(S)=\binom{5}{2}=10
\Rightarrow P(E)=\frac{n(E)}{n(S)}=\frac{4}{10}=\frac{2}{5}

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