Question

From a bag containing 3 pencils, 2 rubbers, and 3 pens, a random sample of 4 pieces of stationary is selected. If X is the number of pencils and Y is the number of rubbers in the sample, find the joint probability distribution of X and Y? 

Answer 1

Let pencils = A

Rubbers = B

Pens = C

We have 10 variants:

AAAB: X=3, Y=1

AAAC: X=3, Y=0

AABB: X=2, Y=2

AACC: X=2, Y=0

AABC: X=2, Y=1

ACCC: X=1, Y=0

ABCC: X=1, Y=1

ABBC: X=1, Y=2

BBCC: X=0, Y=2

BCCC: X=0, Y=1

The joint probability distribution of X and Y:

P(X=3, Y=1) = P(X=3, Y=0) = P(X=2, Y=2) = P(X=2, Y=0) = P(X=2, Y=1) = P(X=1, Y=0) = P(X=1, Y=1) = P(X=1, Y=2) = P(X=0, Y=2) = P(X=0, Y=1)  $= \dfrac{1}{10}$