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Question

A box contains 10 red marbles, 20 blue marbles and 30 green marbles. 5 marbles are drawn at random. From the box, what is the probability that : 

(i) all are blue? 

(ii) at least one is green? 


Solution

Out of 60 marbles, five marbles can be draw in 60C5 ways.

  Total number of elementary events =60C5

(i) Out of 20 blue marbles, five blue marbles can be chosen in 20C5 ways. 

Favourable number of events =20C5 ways 

Hence, the required probability is given by
20C560C5=20×19×18×17×1660×59×58×57×56

=19×6×1759×29×57×7=2×1759×29×7=3711977

(ii) P (no green) =Favorable outcomesTotal outcomes=30C560C5

Thus, P (at least one green)=1-P (no green)

=130C560C5

=11174484

=44841174484=43674484


 

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