Probability Question 273
Question: Probability that India will win against Pakistan in a cricket match is 2/3, in series of 5 matches what is the probability that India will win the series?
Options:
A) $ 161/81 $
B) $ 192/243 $
C) $ 172/243 $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
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){{( \frac{2}{3} )}^{3}}{{( \frac{1}{3} )}^{2}} $ R
equired probability $ =P(3)+P(4)+P(5) $
$ ={{(}^{5}}C_3){{( \frac{2}{3} )}^{2}}{{( \frac{1}{3} )}^{2}}+{{(}^{5}}C_4){{( \frac{2}{3} )}^{4}}{{( \frac{1}{3} )}^{1}} $
$ +{{(}^{5}}C_5){{( \frac{2}{3} )}^{5}}{{( \frac{1}{3} )}^{0}} $
$ =\frac{10'8}{243}+\frac{5'16}{243}+\frac{1'32}{243}=\frac{192}{243} $
BETA
