Question

In a race, the odd favor of horses P, Q, R and S are 1 : 3, 1 : 4, 1 : 5 and 1 : 6 respectively. Find the probability that one of them wins the race.
1. 319/420
2. 313/420
3. 319/421
4. 317/420
5. 321/420

Answer 1

Correct Answer - Option 1 : 319/420

Concept used:

Classical definition of probability.

Formula used:

Probability = Favorable Outcome/Total Outcome.

P(E) = n(E)/n(S)

Calculation:

P(P) = 1/4    

P(Q) = 1/5

P(R) = 1/6

P(S) = 1/7

All the events are mutually exclusive hence,

so probability that atleast one of them lines is given by P(A∪B∪C∪D)

Required probability = P(P) + P(Q) + P(R) + P(S)

⇒ 1/4 + 1/5 + 1/6 + 1/7

⇒ 319/420

∴ The probability that one of them wins the race is 319/420.