Answer:

Probability is all about finding the num of elements in sample space ( i.e all the possibilities that are equally likely ) and the num of elements that favors the event. ( Event is a subset of the sample space )

Let me show the solution in 2 ways

Using Formula :

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| Sample Space| = 6 choose 2 = 6! / (6–2)! * 2! = 15

P(No 2 Red balls)= 3 choose 2 / 15 = 3/15 = 0.2

So the probability P(At least 1 Red Ball) = 1–0.2 = 0.8

Brute Force method

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Let us find out the sample space :

We have 3 red balls - R1,R2,R3 , 1 Y ball - Y1 , 2 GREEN balls - G1,G2

We have to pick 2 balls from 6 balls. The NUMBER of ways that this can be done is calculated as below

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We have place 2 holders :

The first one COULD be filled by any of the balls, R1,R2,R3,Y1 ,G1,G2 i.e 6 ways

The second could be filled by the remaining 5 balls i.e 5 ways

so we have 6*5=30 ways of picking the balls. Since the SEQUENCE does not MATTER i.e R1R2 and R2R1 are same etc. we need to divide 30 by number of ways that 2 elements can be arranged which is 2!=2