# The probability of India winning a test match against the west indies is 1/2 assuming independence from match to match. The probability that in a match series India’s second win occurs at the third test is

## Solution :

Let $$A_1$$, $$A_2$$, $$A_3$$ be the events of match winning in first, second and third matches respectively and whose probabilities are

P($$A_1$$) = P($$A_2$$) = P($$A_2$$) = $$1\over 2$$

$$\therefore$$  Required Probability

= P($$A_1$$)P($$A_2’$$)P($$A_3$$) + P($$A_1’$$)P($$A_2$$)P($$A_3$$)

= $$({1\over 2})^3$$ + $$({1\over 2})^3$$  = $$1\over 8$$  + $$1\over 8$$ = $$1\over 4$$

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