Probability of die rolls

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

  1. boks

    Thread Starter Active Member

    Oct 10, 2008
    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
    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.