Probability help

• Nov 16th 2012, 05:25 PM
gfbrd
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
• Nov 16th 2012, 10:18 PM
chiro
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.
• Nov 16th 2012, 10:24 PM
gfbrd
Re: Probability help
is it possible if you can show me it using the principle of inclusion-exclusion?
• Nov 16th 2012, 10:31 PM
chiro
Re: Probability help
Can you state the definition in your book/notes?
• Nov 16th 2012, 11:00 PM
gfbrd
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|
• Nov 16th 2012, 11:16 PM
chiro
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.
• Nov 17th 2012, 12:01 AM
gfbrd
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
• Nov 17th 2012, 11:47 AM
Plato
Re: Probability help
Quote:

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 $1-\mathcal{P}(F\cup T)$.
• Nov 17th 2012, 08:33 PM
gfbrd
Re: Probability help
thanks plato but the problem is that i dont really understand how to apply it to the formula from above =/