## Saturday, 29 October 2011

### Puzzle-14 (XAT-2010)

The chance of India winning a cricket match against Australia is 1/6. What is the minimum number of matches India should play against Australia so that there is a fair chance of winning at least one match?
(A)3      (B) 4        (C) 5        (D) 6   (E) None of these
Solution follows here:

Solution:
Winning in at least one match is – winning in only one match or winning in two matches or winning in three matches etc etc., winning in all matches. Hence, to find probability for winning in at least one match, we find complement of “losing in all matches”:
Given, Probability that India wins = 1/6 => Probability that India loses = 1-(1/6) = 5/6
For fair chance of winning, the probability should be ≥ 0.5
Now we proceed for finding minimum number of matches required for fair chance of winning:
 Number of matches Probability of losing all matches Probability of winning in at least one 1 5/6 1-(5/6) = 1/6 < 0.5 2 (5/6)*(5/6) = 25/36 1-(25/36) = 11/36 < 0.5 3 (5/6)*(5/6)*(5/6) = 125/216 1-(125/216) = 91/216 < 0.5 4 (5/6)*(5/6)*(5/6)*(5/6) = 625/1296 1-(625/1296) = 671/1296 > 0.5

Hence a minimum of 4 matches required for India for fair chance of winning.