Question

(ii) Four horses A, B, C, D were participating in a race. Each horse has equally likely
chance of winning the race and only one horse will be declared as winner. The
chance of 'A' winning the race is twice of 'B' winning the race. The chance of 'B'
winning the race is thrice of 'C' winning the race. The chance of 'C' winning the
race is four times of 'D' winning the race. If P(A) + P(B) + P(C) + P(D) = 1 then find
the probabilities of each horse winning the race.
11​

Answer 1

The probability of A winning the race = 24/41

The probability of B winning the race = 12/41

The probability of C winning the race = 4/41

The probability of D winning the race = 1/41

Let the probability of D winning the race be x.

C's winning probability is equal to 4x

B's winning probability is equal to 12x

A's winning probability is equal to 24x

Given that P(A) + P(B) + P(C) + P(D) = 1

=> x + 4x + 12x + 24x = 1

=> 41x = 1

=> x = 1/41

Value of 4x = 4/41 , 12x = 12/41 , 24x = 24/41