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Question

(B) Total number of marbles $= 4 + 5 + 2 + 3 = 14$.Total number of ways to draw $3$ marbles from $14$ is ${}^{14}C_{3} = \frac{14 	imes 13 	imes 12}

Vedclass · Accepted Answer

$\frac{199}{364}$

Vedclass · Answer

(B) Total number of marbles $= 4 + 5 + 2 + 3 = 14$.Total number of ways to draw $3$ marbles from $14$ is ${}^{14}C_{3} = \frac{14 	imes 13 	imes 12}{3 	imes 2 	imes 1} = 364$.Number of non-yellow marbles $= 14 - 3 = 11$.Number of ways to draw $3$ marbles such that none of them is yellow is ${}^{11}C_{3} = \frac{11 	imes 10 	imes 9}{3 	imes 2 	imes 1} = 165$.Probability that no marble is yellow $= \frac{165}{364}$.Probability that at least $1$ marble is yellow $= 1 - P(	ext{no yellow marble}) = 1 - \frac{165}{364} = \frac{364 - 165}{364} = \frac{199}{364}$.

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 at least $1$ is yellow?

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