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.

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.

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?

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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?

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How many cards are both a Jack and Black?

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

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

galactus said:

Use the add property when you see OR.

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

pka said:

galactus said:

Use the add property when you see OR.

Click to expand...

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

Click to expand...

Yes, I should have stated that.