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Home  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class12  >>  Probability

The probability that England wins a cricket match against India is $ \large\frac{1}{3}$. If India and England play 3 test matches the probability that India will win exactly 2 test matches is

$\begin {array} {1 1} (A)\;\large\frac{1}{3} & \quad (B)\;\large\frac{4}{9} \\ (C)\;\large\frac{5}{9} & \quad (D)\;None \: of \: these \end {array}$

 

1 Answer

Here $ n = 3$
P = P ( India wins one match against England )
$ = \large\frac{2}{3}$
$ Q = \large\frac{1}{3}$
$ \therefore P(2) = 3C_2 \bigg( \large\frac{2}{3} \bigg)^2 \bigg( \large\frac{1}{3} \bigg)^1$
$ = \large\frac{12}{27}$
$ = \large\frac{4}{9}$
Ans : B
answered Jan 4, 2014 by thanvigandhi_1
 

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