Q. 255.0( 1 Vote )

# An urn contains 5

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. ∑(p_{i}) = 1 where p_{i} is probability associated with x_{i}

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 p_{i} and x_{i.}

Clearly, ∑(p_{i}) =

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

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