Find the probability that India wins exactly one of the first three matches ........

Quantitative Aptitude ( CCS) Case Studies

Direction : Study the following information and answer the questions that follow:

In a bilateral cricket series between India and Australia, the probability that India wins the first game is 0.4. If India wins any game, the probability that it wins the next game is 0.3; otherwise the probability is 0.2.

Find the probability that India wins exactly one of the first three matches.

0.416

0.396

0.096

0.404

0.214

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Explanation:

This problem can be solved in three parts
Part 1- India wins first game and loses second and third
part 2= Lose + Win + Lose
Part 3= Lose + Lose+ Win
P (Part 1)= India wins first game * India loses second game* India loses third game
= 0.4 * (1-0.3)* (1-0.2)= 0.4*0.7*0.8 = 0.224
P (Part2)= India loses first game * Wins second game * Loses third game
= (1-0.4)* 0.2 * (1-0.3)= 0.6*0.2*0.7= 0.084
P (Part 3)= L*L*W = (1-0.4)* (1-0.2) * 0.2= 0.6*0.8*0.2= 0.096
P= P1+P2+P3= 0.404

Hence, option 4 is the correct answer.