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  4. India and Pakistan play a 5 match test series of hockey, the probability that India wins at least three matches is :

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Q. India and Pakistan play a 5 match test series of hockey, the probability that India wins at least three matches is :

Probability

Solution:

India win atleast three matches
$ = ^{5}C_{3} \left(\frac{1}{2}\right)^{5} + ^{5}C_{4} \left(\frac{1}{2}\right)^{5} + ^{5}C_{5} \left(\frac{1}{2}\right)^{5} $
$= \left(\frac{1}{2}\right)^{5} \left(16\right) = \frac{1}{32} \times16 = \frac{1}{2} $