We throw three healthy dice together.

dazhebhs

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

Please be complete. Thank you!

Eliz.
 
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].
 
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.
 
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)
 
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