When to use addition or multiplication in probability?

[bullshark818]

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.

Also, I'm just simply confused about when exactly I am supposed to use the addition or multiplication rules. I know what the rules are, just not when I am supposed to use one or the other.

Thanks in advance if you can help me.

 

[soroban]

Hello, bullshark818!

With problems as simple as these two, don't worry about multiplication/addition.

There are 52 possible outcomes, right?

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

How many cards are Fours or Diamonds?

\(\displaystyle \text{There are 4 Fours: }\:4\heartsuit,\:4\spadesuit,\:4\diamondsuit,\:4\clubsuit\)

\(\displaystyle \text{There are 13 Diamonds: }\:A\diamondsuit,\:2\diamondsuit,\:3\diamondsuit,\:4\diamondsuit,\:5\diamondsuit,\:6\diamondsuit,\:7\diamondsuit,\:8\diamondsuit,\:9\diamondsuit,\:10\diamondsuit,\:J\diamondsuit,\:Q\diamondsuit,\:K\diamondsuit\)

\(\displaystyle \text{Hence, there are }16\text{ cards which are Fours or Diamonds.}\)
. . \(\displaystyle \text{(Don't count the }4\diamondsuit\text{ twice!)}\)

\(\displaystyle \text{Therefore: }\(\text{4 or Diamond}) \;=\;\frac{16}{52} \;=\;\frac{4}{13}\)

When drawing a single card, what is the probability of getting a Jack and a Black card?

How many cards are both a Jack and Black?

\(\displaystyle \text{Only two: }\:J\spadesuit,\:J\clubsuit\)

\(\displaystyle \text{Therefore: }\(\text{Jack and Black}) \;=\;\frac{2}{52} \;=\;\frac{1}{26}\)

 

[pka]

Use the add property when you see OR.

That is true if the two events are disjoint(mutully exclusive). You can just add the two.

 

[galactus]

Use the add property when you see OR.

That is true if the two events are disjoint(mutully exclusive). You can just add the two.

Yes, I should have stated that.