1. ## Probability help

Hey there I need some help with this problem

A random number generator randomly generates the integers 1, 2, . . . , 9 with equal probability. Find the probability that after n numbers are generated the product is a multiple of 10.

Hoping someone can guide me through this problem so I can understand how to do this thanks

2. ## Re: Probability help

Hey gfbrd.

There are standard results for product distributions:

Product distribution - Wikipedia, the free encyclopedia

The best way IMO to approach this is to find the logarithm of the discrete uniform random variable, find the convolution of those distributions and see if it has the same or a general form, and then do a variable transformation by calculating e^Z where Z is the sum of all logarithmic uniform variables to get the answer.

3. ## Re: Probability help

is it possible if you can show me it using the principle of inclusion-exclusion?

4. ## Re: Probability help

Can you state the definition in your book/notes?

5. ## Re: Probability help

here is the equation for 3 sets
|A∪B∪C| = |A| + |B| + |C| - |A∩B| - |B∩C| - |A∩C| + |A∩B∩C|

6. ## Re: Probability help

I think I see what they want you to do.

Try considering all events where the product is ten and then finding the probability of the union of all those events.

7. ## Re: Probability help

the only time if you get a product of 10 is if the number is even and multiplied by 5 vice versa

8. ## Re: Probability help

Originally Posted by gfbrd
the only time if you get a product of 10 is if the number is even and multiplied by 5 vice versa
Let $F$ be the event that no multiple of five is generated.
Let $T$ be the event that no multiple of two is generated.

Then find $1-\mathcal{P}(F\cup T)$.

9. ## Re: Probability help

thanks plato but the problem is that i dont really understand how to apply it to the formula from above =/