statistics

Question

Suppose I roll a one four-sided die and one six-sided die. Let X be the sum of the dots showing on two die. How do I find the probabilty distribution of X?

Answer 1

Deion, I assume that the four-sided die is marked 1 to 4 on its respective sides

 

Systematically go through each combination of the dice and assign a probability to each

 

For instance, what is the probability of rolling a combination that adds to 1?  zero

 

What is the probability of getting a combination adding to two?  (snake eyes):    1/4 * 1/6 = 1/24  

This is where die #1 shows a 1 (1/4 chance) followed by die #2  showing a 1 (1/6 chance)

 

What is the probability of  getting a combination of the dice adding to three  (1+2) or (2+1)?  1/4 * 1/6 + 1/4 * 1/6 = 2/24

 

Now what is the probability of getting a combination adding to four (1+3), (3+1), (2+2)?

 

Do this for every possible combination up to 10 which would be the maximum sum. Now make a bar chart (histogram) of probability on the vertical axis vs sum of the dice on the horizontal axis. This is the probability distribution for these two dice. have fun!