Question

Roll three fair dice. Find the probability mass function of the product of the three numbers appearing given that their sum is 5.

Answer 1

Just as one die has six outcomes

If we roll n dice then there are 6n outcomes.

and two dice have 62 = 36 outcomes

the probability experiment of rolling three dice has 63 = 216 outcomes.

sample space total number is 216

event occue succefull outcome is

event={(3,1,1),(1,3,1),(1,1,3),(2,2,1),(2,1,2),(1,2,2)}

event occure 6 times

Probability of a sum of 5: 6 / 216 = 2.8%

event occure 6 times

Probability mass function (given that their sum is 5)

x 1 2 3 4 5 6

p(x) 1/6 1/6 1/6 1/6 1/6 1/6

thanks