# When to use addition or multiplication in probability?

• Jun 21st 2011, 04:15 AM
bullshark818
When to use addition or multiplication in probability?
I am confused about "and" and "or" problems. For example:

When drawing a single card, what is the probability of getting a 4 or a diamond?

When drawing a single card, what is the probability of getting a jack and a black card?

Do the words and/or dictate whether or not I am supposed to use addition or multiplication? My teacher has not done a good job of explaining this.

Thanks in advance if you can help me. (Smile)
• Jun 21st 2011, 06:41 AM
Plato
Re: When to use addition or multiplication in probability?
Quote:

Originally Posted by bullshark818
I am confused about "and" and "or" problems. Do the words and/or dictate whether or not I am supposed to use addition or multiplication? My teacher has not done a good job of explaining this.

Actually those words have very little relation to the usage of addition or multiplication.

The most widely used set of axioms for probability contains three axioms. One theorems we can prove is: $\mathcal{P}(A\text{ or }B)= \mathcal{P}(A)+ \mathcal{P}(B)- \mathcal{P}( A\text{ and }B).$

I chose that theorem to illustrate the ‘mixed’ nature of your question.

Let’s examine those two words.
$\mathcal{P}( A\text{ and }B)$ means the probability of both events $A~\&~B$ occurring together. Both happen.

On the other hand, $\mathcal{P}( A\text{ or }B)$ means the probability of at least one of the events $A~\&~B$ occurs. One or both happen.

Finding what $\mathcal{P}( A\text{ and }B) =~?$, can be easy or difficult.
If events $A~\&~B$ are independent then $\mathcal{P}( A\text{ and }B)= \mathcal{P}(A)\cdot \mathcal{P}(B)$.

But if they are dependent then things get more complicated.

So you need to stay tuned in the course for what is to come.