# Thread: Conditional Probability #2

1. ## Conditional Probability #2

Three dice, one large, one medium and one small, are rolled. A is the event when the large die shows an odd number, B is the event when the medium die shows an odd number, and C is the event when the small die shows an even number. Determine if the events are independent or dependent.

Why is $p(A\cap B\cap C)=\frac{1}{8}$?

2. Originally Posted by chengbin
Three dice, one large, one medium and one small, are rolled. A is the event when the large die shows an odd number, B is the event when the medium die shows an odd number, and C is the event when the small die shows an even number. Determine if the events are independent or dependent. Why is $p(A\cap B\cap C)=\frac{1}{8}$?
Because the events independent.
$P(A\cap B\cap C)=P(A)P(B)P(C)=\frac{1}{8}$

3. Besides knowing it is independent.

I had to do this first, then do $p(A)\cdot p(B)\cdot p(C)$ to prove it is independent.

4. Originally Posted by chengbin
Besides knowing it is independent.
I had to do this first, then do $p(A)\cdot p(B)\cdot p(C)$ to prove it is independent.
I have no idea what that means.
But if we roll n dice of any size or color, the probability that they all show an even number is $2^{-n}$.
The events are clearly independent. There is nothing to prove.

5. What I meant was, I have to find out the value of $p(A\cap B\cap C)$ first, then find the value of $p(A)\cdot p(B)\cdot p(C)$ to verify it is independent.

I'm just starting with probability, so we're doing simple stuff.

6. Originally Posted by chengbin
What I meant was, I have to find out the value of $p(A\cap B\cap C)$ first, then find the value of $p(A)\cdot p(B)\cdot p(C)$ to verify it is independent.
I'm just starting with probability, so we're doing simple stuff.
Your problem is simple: you do not know what the word independent means when use in probability.

7. Originally Posted by Plato
Your problem is simple: you do not know what the word independent means when use in probability.
Yeah, you're right.

Now I'm trying to find an article on this...

8. Originally Posted by chengbin
Yeah, you're right.

Now I'm trying to find an article on this...
Simply do this thought experiment: If you roll Dice A, will it's outcome in any way shape or form, effect Dice B's roll? We will even roll them in separate rooms, to remove one die from hitting another or some silliness like that.

The probability of A and B and C is (1/8). The P(A) is 1/2; the P(B) is 1/2; the P(C) is 1/2.