The probability that Australia wins a match against India in a cricket game is given to be $\frac{1}{3}$ . If India and Australia play 3 matches, what is the probability that
i) Australia will loose all the three matches?
ii) Australia will win atleast one match?

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Detailed Solution

$P (A) = P (A u s t r a l i a w i n s a m a t c h a g a i n s t I n d i a)$

$= 1 / 3$

i) probability of Australia will loose all 3 matches

$= (P (\bar{A}))^{3} = {(\frac{2}{3})}^{3} = \frac{8}{27}$

ii) $P$ (Australia will win at least one match)

$= 1 - P (Australia will loose all three matches)$

$= 1 - \frac{8}{27} = \frac{19}{27}$

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