Question

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
1. 3 / 5
2. 1 / 5
3. 2 / 5
4. 4 / 5

Answer 1

Correct Answer - Option 3 : 2 / 5

Concept:

P(A) is the probability of an event “A” = \(\rm \dfrac {n(A)}{n(S)}\)

Where n(A) is the number of favourable outcomes and n(S) is the total number of events in the sample space.

Calculations:

Give, there are 5 horses say H1, H2, H3, H4, H5

Mr. A selects two of the horses at random and bets on them

Selection of horses can be done H1H2 , H1H3, H1H4, H1H5, H2H3 ,H2H4, H2H5, H3H4, H3H5, H4H5 = 10 ways.

 

Only one horse say H3  can win = H1H3 , H2H3,  H3H4, H3H5 = 4 ways 

 

The probability that Mr. A selected the winning horse is = \(\dfrac 4 {10}\) = \(\dfrac 2 5\)​