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× 2 P(C)

4 P(C)

2 P(C)

Let probabilities of horses A, B and C be P (A), P (B), and P (C).

P (A) = 2P (B) .......(i)

P (B) =

Substituting (ii) in (i),

P (A) = 2

∴P (A) =

Assuming only one of them is going to win the race

∴ P (A) + P (B) + P (C) = 1

∴ 7P (C) = 1

P(B)

4 P(C)

.....(iii)

2 P(C)

.....(ii)

∴

Q. Three horses A, B and C are in a race, A is twice as like to win as B

and B is twice as like to win as C, what are their probabilities of winning ?

Substituting the value of P (C) in (iii),

P (A) =

+ P (C)

= 1

∴

Substituting the value of P (C) in (ii),

P (B) =

Probability of horse C winning the race

Probability of horse A winning the race

Probability of horse B winning the race

Sol.

Since we don’t know anything about the ability of the horses

Probabilty of Horse A winning the race or Horse B winning the race or Horse C winning the race are equally likely to occur

Hence they are elementary events

We know sum of probabilities of all elementary events = 1

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