Question

An urn contains 6 red, 4 blue, 2 green and 3 yellow marbles. if two marbles are picked at random, what is the probability that either both are green or both are yellow

Answer 1

Total number of marbles = 6 + 4 + 2 + 3 = 15

Number of green = 2

Number of yellow = 3

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P(both green or both yellow) = (2/15) (1/14) + (3/15)(2/14) = 1/105 + 1/35 = 4/105

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Answer: 4/105

Answer 2

Answer:

Probability that either both are green or both are yellow is 4/105.

Step-by-step explanation:

Given:

Number of Red marbles in Urn = 6

Number of Blue marbles in Urn = 4

Number of Green marbles in Urn = 2

Number of Yellow marbles in Urn = 3

Two marbles are taken from Urn.

To find: Probability that either both are green or both are yellow

Total Number of Marbles in the Urn = 6 + 4 + 3 + 2 = 15

We use the fact that if a marble is drawn out then it is not replaced that means for next turn there is one marble less in the urn.

let Y represent that Yellow Marble is taken out and G represent that Green Marble is taken out.

Formula used to calculate Probability,

$Probability=\frac{Number\:of\:favorable\:outcome}{Total\:Number\:of\:outcome}$

Required Probability = P(G) × P(G) + P(Y) × P(Y)

                                  $=\frac{2}{15}\times\frac{1}{14}+\frac{3}{15}\times\frac{2}{14}$

                                  $=\frac{2}{210}+\frac{6}{210}$

                                  $=\frac{8}{210}$

                                  $=\frac{4}{105}$

Therefore, Probability that either both are green or both are yellow is 4/105.