1. ## Prove through statistics

I have a problem which says:

Prove through statistics that:

P(A and B) = P(A) x P(B)

How do you prove this through statistics? Thank you for any help you can give me.

2. ## Re: Prove through statistics

Originally Posted by u12480
I have a problem which says:
Prove through statistics that:
P(A and B) = P(A) x P(B)
How do you prove this through statistics? Thank you for any help you can give me.
You have a real problem there.
Because you cannot prove that through statistics or any other way,
It is not true as stated. Are there other conditions that you held back?

3. ## Re: Prove through statistics

The only other "key" that was part of the instructions was that we had to include the conditional prob. formula in some form. That was it. Pretty tough for a new statistics student.

4. ## Re: Prove through statistics

Originally Posted by u12480
The only other "key" that was part of the instructions was that we had to include the conditional prob. formula in some form. That was it. Pretty tough for a new statistics student.
Well it is still no true unless you are given that exents $\displaystyle A~\&~B$ are independent.

5. ## Re: Prove through statistics

To figure this out (new at statistics) can we assume they are independent and then what would that mean?

6. ## Re: Prove through statistics

Originally Posted by u12480
To figure this out (new at statistics) can we assume they are independent and then what would that mean?
The symbol $\displaystyle \mathcal{P}(B|A)$ is read the probability of B given A.
The probability is calculated by $\displaystyle \mathcal{P}(B|A)=\frac{\mathcal{P}(A\cap B)}{\mathcal{P}(A)}$.

If we know that $\displaystyle A~\& B$ are independent that means $\displaystyle \mathcal{P}(B|A)=\mathcal{P}(B)$.
That would $\displaystyle \mathcal{P}(B\cap A)=\mathcal{P}(B)\mathcal{P}(A)$.