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 ______.

Options

• `2/5`

• `4/5`

• `3/5`

• `1/5`

Answer 1

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 `underlinebb(2/5)`.

Explanation:

Let 5 horses be H₁, H₂, H₃, H₄ and H₅.

Total ways of selecting pair of horses be

= ⁵C₂

= 10[i.e. H₁H₂, H₁H₃, H₁H₄, H₁H₅, H₂H₃, H₂H₄, H₂H₅, H₃H₄, H₃H₅, H₄H₅]

Any horse can win the race in 4 ways

(e.g. for H₁ : H₁H₂, H₁H₃, H₁H₄, H₁H₅)

Hence required probability = `4/10` = `2/5`