# 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:11

## 7 Answers

Aman Bansal
592 Points
9 years ago

Dear Shiva,

The probability of winning is 2/5

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upender surepally
126 Points
9 years ago

2/5

Shaurya Gupta
41 Points
9 years ago

total no of options - 5

selected options - 2

therefore probability that Mr.A selected the winning horse - 2/5

Aravind Bommera
36 Points
9 years ago

The probability of winning is 2/5

ishaan agarwal
8 Points
8 years ago
This question came in aieee 2003. 2/5 is not in the option only.
R Surya Narayan
13 Points
5 years ago
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
$n(E)=\binom{4}{1}=4$
$n(S)=\binom{5}{2}=10$
$\Rightarrow P(E)=\frac{n(E)}{n(S)}=\frac{4}{10}=\frac{2}{5}$

ankit singh
askIITians Faculty 614 Points
2 years ago
In total there are 5 horses. out of these Mr A selects two horses. This can be done in 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 4C1=4 ways.
Thus,

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
$n(E)=\binom{4}{1}=4$
$n(S)=\binom{5}{2}=10$
$\Rightarrow P(E)=\frac{n(E)}{n(S)}=\frac{4}{10}=\frac{2}{5}$

The probability that Mr.A selected the winning horse is = 104=52In total there are 5 horses. out of these Mr A selects two horses. This can be done in 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 4C1=4 ways.
Thus,
The probability that Mr.A selected the winning horse is = 104=52

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