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.
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 pi and xi.
∴ Now we are ready to write the probability distribution for X:-
The following table gives probability distribution: