Find the probability distribution of the number of white balls drawn in a random draw of 3 balls without replacement, from a bag containing 4 white and 6 red balls.
Let X denote the number of white balls drawn in a random draw of 3 balls.
∴ X can take values 0,1,2 or 3.
Since bag contains 6 red and 4 white ball, i.e. at a total of 10 balls
∴ total no. of ways of selecting 3 balls out of 10 = 10C3
For selecting 0 white balls, we will select all 3 balls from red
∴ P(X = 0) = P (not selecting any white ball) =
For selecting 1 white ball, we will select all 2 balls from red and 1 from white
∴ P(X = 1) =
For selecting 2 white balls, we will select all 1 ball from red and 2 from white
∴ P(X = 1) =
For selecting 3 white balls, we will select all 0 balls from red and 2 from white
∴ P(X = 1) =
Now we have pi and xi.
∴ Now we are ready to write the probability distribution for X:-
The following table gives probability distribution: