# Thread: Prob. Distribution problem. Help Please.

1. ## Prob. Distribution/Random Variable problem

Roll a dice 4 times
X = smallest face observed
Given P(X=6) = 1/1296

Find:
P(X=1)
P(X=2)
P(X=3)
P(X=4)
P(X=5)

I got 216/1296, 125/1296, 64/1296, 27/1296, and 8/1296 for P(X=1) through P(X=5) respectively. I think I did something wrong as the numerators don't add up to 1296 like I thought they would.

Help is appreciated.

This is a probability distribution function by the way.

2. show your work
For the event X=1, that means you had at least one 1.

so $P(X=1)=1-P({\rm no}\quad 1's)=1-(5/6)^4$

3. Originally Posted by matheagle
For the event X=1, that means you had at least one 1.

so $P(X=1)=1-P({\rm no}\quad 1's)=1-(5/6)^4$
Here's my for the solutions in the first post:

4. what about switching the order?

5. Originally Posted by matheagle
what about switching the order?
What order? I'm so confused on how to do this. I know how to get P(X=1) but how do I get P(X=2) and so on?

6. I know I must be missing something because I didn't think this was supposed to be this hard of a problem.

7. $P(X=2)=4(1/6)(5/6)^3$
You keep assuming that the first toss is a two, it can be a 3,3,3,2.
So there are 4 places to put down a 2.