A basket contains 10 red balls and 4 white balls. If three balls are taken from the basket one after the other, determine the possible values of the random variable R representing the number of the red balls

We first define the sample space as below

S = { RRR, RRW, RWR, WRR, WWR, WRW, RWW, WWW}

we then count the number of red balls in each outcome and assign a number to the outcome as below

Outcomes The value of R

RRR 3

RRW 2

RWR 2

WRR 2

WWR 1

WRW 1

RWW 1

WWW 0

Hence, we may conclude that the values of the random variables R (number of red balls ) are 0, 1, 2 and 3.