Q4 of 23 Page 1

Attempt any two subquestions form the following:

In a certain race there are three girls X,Y,Z. The winning probability of X is twice than Y and the winning probability of Y is twice than Z. If P(X) + P(Y) + P(Z) = 1, then find the winning probability of each girl.

Given:

Let X wins, P(X) = 2 × P(Y)


Y wins, P(Y) = 2 × P(Z)


Z wins, P(Z) = P(Z)


Assume Z wins 1 times,


P(Z) = 1


P(Y) = 2 × P(Z) = 2


P(X) 2 × P(Y) = 2 × 2 = 4


Now, Total probability P(S) = P(X) + P(Y) + P(Z)


= 1 + 2 + 4 = 7


Probability of X wins = 4/7


Probability of Y wins = 2/7


Probability of Z wins = 1/7


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