# Probability of die rolls

Discussion in 'Math' started by boks, Jan 9, 2009.

1. ### boks Thread Starter Active Member

Oct 10, 2008
218
0
Consider an experiment that consists of 2 rolls of a balanced die. If X is the number of 4s and Y is the number of 5s obtained in the 2 rolls of the die, find the joint probability function.

$f(x,y) = \frac{(_{2}C_{x})(_{2}C_{y})}{36}$

because there are $_{2}C_{x}$ ways to combine x 4s and $_{2}C_{y}$ ways to combine y 5s, and 36 possible combinations from a throw with 2 dice.

However, this formula doesn't give me the correct probability distribution of X and Y. What's my mistake?

2. ### steveb Senior Member

Jul 3, 2008
2,433
469
I can't follow what you are saying. What is Cx and Cy?

The only nonzero values of the joint prob function will occur for the following cases:

x=0, y=0
x=0, y=1
x=1, y=0
x=1, y=1
x=0, y=2
x=2, y=0

Note that x or y can be 0, 1 or 2 but x and y can not both be 2.

You should be able to calculate the probability of each case, noting that the sum of all probablities should add to 1.