Question
A bag contains 2 white and 1 red balls. One ball is drawn at random and then put back in the box after noting its colour. The process is repeated again. If X denotes the number of red balls recorded in the two draws, describe X.
Solution
Let the balls in the bag be denoted by w1, w2, r.
∴ S = {w1 w1 , w1 w2 , w2 w2, w2 w1, w1 r, w2 r, r w1, r w2, r r}
Now, for ω ∈ S
X(ω) = number of red balls
∴ X({w1 w1}) = X({w1 w2}) = X({w2 w2}) = X({w2 w1}) = 0
X({w1 r}) = X({w2 r}) = X({r w1}) = X({r w2}) = 1
and X({r r}) = 2
∴ X is a random variable which can take values 0, 1 or 2.
