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:
(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.
Answer (B)
No comments:
Post a Comment