Let X denote the number of red balls drawn in a random draw of 4 balls.

∴ X can take values 0,1,2,3 or 4.

Since bag contains 8 red and 4 white balls i.e. at a total of 12 balls

∴ total no. of ways of selecting 4 balls out of 12 = 12C₄

For selecting 0 red balls we will select all 3 balls from red

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

For selecting 1 red ball, we will select 1 ball from 8 red and 3 balls from 4 white

∴ P(X = 1) =

For selecting 2 red ball, we will select 2 balls from 8 red and 2 balls from 4 white

∴ P(X = 2) =

For selecting 3 red ball we will select 3 balls from 8 red and 1 ball from 4 white

∴ P(X = 3) =

∴ P(X = 4) = P (selecting all red 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: