I'm not really sure how to go about this, so any help would be greatly appreciated!
Suppose you throw a six-sided die five times. Find the probability that the sum of the outcomes of the throws is 15 using generating functions.
I'm not really sure how to go about this, so any help would be greatly appreciated!
Suppose you throw a six-sided die five times. Find the probability that the sum of the outcomes of the throws is 15 using generating functions.
You can use:
When you expand it out, the coefficient of x^15 is your answer.
Doing so, we see the coefficient of x^15 is 651.
The total number of outcomes is
Therefore, the probability of getting a sum of 15 is
Oops, CB beat me. Oh well, same conclusion. That's good.
The thing to do is use a calculator that'll expand. But, if you must do it the long way.
Since,
We take note that we factored out a x^5. Therefore, we need only look for x^10 terms, instead of x^15.
When we multiply we get:
Looking at this we can see the terms:
are the terms which have the x^10 term when we multiply.
(-5)(70)+1001=651