Question 97

# 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 atleast one match?

Solution

Let the number of matches that India needs to play = $$x$$

Now, if $$1 - (\frac{5}{6})^x \geq \frac{1}{2}$$ , we can consider that India has a fair chance of winning the match.

=> $$(\frac{5}{6})^x \leq \frac{1}{2}$$

If, $$x = 3$$, we get $$\frac{125}{216}$$, which is greater than $$\frac{1}{2}$$

If, $$x = 4$$, we get $$\frac{625}{1296}$$, which is less than $$\frac{1}{2}$$

$$\therefore$$ The number of matches that India needs to play must be atleast 4