Verified answer

★Given:-

• Three horses A, B and C are in a race

• A is twice as likely to win as B

• B is twice as likely to win as C

★To find:-

• Their probability of winning.

★Solution:-

Assume,

• Probability of winning of C = x

As, B is twice as likely to win as C,

• Probability of winning of B = 2x

As,A is twice as likely to win as B,

• Probability of winning of A :-

⇒ 2×P(B) = 2× 2x = 4x.

Total probability of winning=1

Hence,

⇒ x + 2x + 4x = 1

⇒ 7x = 1

⇒ x = 1/7

Therefore,

→Probability of C = 1/7

→Probability of winning of B = 2x

⇒ 2 × (1/7)

⇒ 2/7

∴ Probability of B is 2/7

→Probability of winning of A=4x

⇒ 4 × (1/7)

⇒ 4/7

∴Probability of A = 4/7

Hence,

The probabilities of A,B,C are 4/7,2/7,1/7 respectively.

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