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(D) Total number of marbles = $4 + 5 + 2 + 3 = 14$.Total number of ways to draw $3$ marbles from $14$ is given by ${}^{14}C_{3} = \frac{14 	imes 13 \

Vedclass · Accepted Answer

$\frac{30}{91}$

Vedclass · Answer

(D) Total number of marbles = $4 + 5 + 2 + 3 = 14$.Total number of ways to draw $3$ marbles from $14$ is given by ${}^{14}C_{3} = \frac{14 	imes 13 	imes 12}{3 	imes 2 	imes 1} = 364$.We want to find the probability that none of the $3$ marbles is green.This means all $3$ marbles must be chosen from the non-green marbles (blue,red,and yellow).Number of non-green marbles = $5 + 2 + 3 = 10$.Number of ways to choose $3$ non-green marbles = ${}^{10}C_{3} = \frac{10 	imes 9 	imes 8}{3 	imes 2 	imes 1} = 120$.Therefore,the required probability = $\frac{	ext{Favourable outcomes}}{	ext{Total outcomes}} = \frac{120}{364}$.Simplifying the fraction by dividing both numerator and denominator by $4$,we get $\frac{30}{91}$.

Study the given information carefully to answer the question that follows. An urn contains $4$ green,$5$ blue,$2$ red and $3$ yellow marbles. If $3$ marbles are drawn at random,what is the probability that none is green?

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