Answer :

The key point to solve the problem:


A variable X is said to be a random variable if the sum of probabilities associated with each value of X gets equal to 1


i.e. ∑(pi) = 1 where pi is probability associated with xi


X represents the number of black balls drawn.


X can take values 0,1 or 2 as both balls drawn can be black which corresponds to X = 2, either of 2 balls can be black which corresponds to X = 1, and if neither of balls drawn is black it corresponds to X = 0


there are a total of 7 balls


n(S) = total possible ways of selecting 2 balls =


P(X = 0) = P(selecting no black balls) =


P(X = 1) = P(selecting 1 black ball and 1 red)


=


P(X = 0) = P(selecting all black balls) =


Now we have pi and xi.



Clearly, ∑(pi) =


X is a random variable, and the above table represents its probability distribution.


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