A) \[161/81\]
B) \[192/243\]
C) \[172/243\]
D) None of these
Correct Answer: B
Solution :
[b] Total number of matches \[=n=5\]India will win the series if it wins either 3 or 4 or 5 matches. In previous egestion we have calculated the value of \[P(3)=\]Probability of winning 3 matches \[={{(}^{5}}{{C}_{3}}){{\left( \frac{2}{3} \right)}^{3}}{{\left( \frac{1}{3} \right)}^{2}}\] Required probability \[=P(3)+P(4)+P(5)\] \[={{(}^{5}}{{C}_{3}}){{\left( \frac{2}{3} \right)}^{2}}{{\left( \frac{1}{3} \right)}^{2}}+{{(}^{5}}{{C}_{4}}){{\left( \frac{2}{3} \right)}^{4}}{{\left( \frac{1}{3} \right)}^{1}}\] \[+{{(}^{5}}{{C}_{5}}){{\left( \frac{2}{3} \right)}^{5}}{{\left( \frac{1}{3} \right)}^{0}}\] \[=\frac{10'8}{243}+\frac{5'16}{243}+\frac{1'32}{243}=\frac{192}{243}\]
You need to login to perform this action.
You will be redirected in
3 sec
