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# An urn contains 4 red and 3 blue balls. Find the probability distribution of the number of blue balls in a random draw of 3 balls with replacement.

Answer :

Let X denote the number of blue balls drawn in a random draw of 3 balls.

∴ X can take values 0,1,2 or 3.

Since bag contains 4 red and 3 blue balls i.e. at a total of 7 balls

∵ balls are drawn with replacement

For selecting 0 blue balls, we will select all 3 red balls

∴ P(X = 0) = P (not selecting any blue ball) =

For selecting 1 blue ball, we will select all 2 red balls and 1 blue

∴ P(X = 1) =

For selecting 2 blue balls, we will select all 1 red ball and 2 blue

∴ P(X = 2) =

For selecting 3 blue balls, we will select all 3 blue and 0 red balls

∴ P(X = 3) = P (selecting all blue ball) =

Now we have p_{i} and x_{i.}

∴ Now we are ready to write the probability distribution for X:-

The following table gives probability distribution:

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