We throw three healthy dice together.

[dazhebhs]

We throw three healthy dice together. If the random variable X is equal to the sum of the numbers on the 3 observation dice. Get the probability function X and find the probability that the sum of the numbers on the dice is at least 15.

 

[stapel]

What are your thoughts? What have you tried? How far have you gotten? Where are you stuck?

Please be complete. Thank you!

Eliz.

 

[pka]

We throw three healthy dice together. If the random variable X is equal to the sum of the numbers on the 3 observation dice. Get the probability function X and find the probability that the sum of the numbers on the dice is at least 15.

If one works with dice, one should learn to use a generating polynomials. SEE HERE.
Each term is the expansion tells about the possible outcomes.
For example: the term [imath]27x^{11}[/imath] tells us there are twenty-seven ways to toss a sum of eleven.
Any term term [imath]\bf{K}x^{{\bf N}}[/imath] tells us there are [imath]\bf{K}[/imath] ways to toss a sum of [imath]\bf{N}[/imath].

 

[Dr.Peterson]

We throw three healthy dice together. If the random variable X is equal to the sum of the numbers on the 3 observation dice. Get the probability function X and find the probability that the sum of the numbers on the dice is at least 15.

I guess that "healthy dice" here means "fair dice", or perhaps "ordinary (6-sided) dice".

In addition to showing work, please tell us what you have learned about probability distributions, so that our advice can be appropriate to what you have learned.

 

[Steven G]

pka clearly gave you the best way to solve the problem.

As a student you need to try something. Other than pka's nice method you should at least try to make a table.
3--1 way (111)
4--3 ways (112, 121, 211)
...
18--1 way (666)