Question

The probability that India wins a cricket test match against England is $\frac{1}{3}$. If India and England play 3 matches, the probability that India will win atleast one match is

• A. $\frac{8}{27}$
• B. $\frac{19}{27}$
• C. $\frac{1}{27}$
• D. $\frac{9}{27}$

Answer 1

Answer: (B)

$\frac{19}{27}$

The probability that India will not win any game $=\frac{2}{3}\times \frac{2}{3}\times \frac{2}{3}=\frac{8}{27}$
The probability that India will win atleast 1 game $=1-$the probability that India will not win any game $=1-\frac{8}{27}=\frac{19}{27}$