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A basket contains 4 red , 5 blue and 3 green marbles . If three marbles are picked at random , what is the probability that at least one is blue ?

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A basket contains 4 red , 5 blue and 3 green marbles . If three marbles are picked at random , what is the probability that at least one is blue ? A. `(7)/(12)` B. `(37)/(44)` C. `(5)/(12)` D. `(7)/(44)` Select the correct answer from above options

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Correct Answer - B Total possible outcomes `=n( S) =""^(12)C_(3)=220` Favourable number of ways of picking 3 marbles (none is blue ) out of 7 marbles `=""^(7)C_(3)=(7xx6xx5)/(1xx2xx3)=35` `implies ` Required probability `=(1-(35)/(220))=(1-(7)/(44))=(37)/(44)`

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