# AP Statistics : How to use the addition rule

## Example Questions

### Example Question #11 : How To Use The Addition Rule

When rolling a 6 sided dice, what is the probability of rolling a 2 or a 4?

Explanation:

In the single roll of a dice, rolling a 2 is mutually exclusive of rolling a 4. When a question asks for the probability of event A "or" event B, the probability is the sum of each event.

First, find the probability of each individual event.

Because the problem asks for a 2 OR a 4, add the indivual probabilities together.

### Example Question #12 : Rules Of Probability

A magician has a bag containing 13 black marbles, 1 red marble, 1 green marble, 1 blue marble, and 1 yellow marble. What is the probability that the magician draws a red or a green marble?

Explanation:

In the draw of a marble, picking a red is mutually exclusive of picking a green marble. When a question asks for the probability of event A "or" event B, the probability is the sum of each event.

First, find the probability of each event occuring.

Because the problem asks for the probability of either red OR green, we add the two probabilities.

### Example Question #12 : How To Use The Addition Rule

A person is drawing a single card from a regular deck of 52 cards. What is the probability that they draw a heart or a spade?

None of the other asnwers are correct.

Explanation:

In a single draw of a card, drawing a heart is mutually exclusive of drawing a spade, so we can use the addition rule to find the probability of a heart of a spade.

First, you must find the probability of each seperate event.

To find the probability of a heart or a spade, just add the probability of each event occuring.

### Example Question #13 : How To Use The Addition Rule

A person draws a single card from a regular deck of 52 playing cards. What is the probability of drawing a heart or a jack?

Explanation:

This problem asks for the probability of one event or another, so we will be using the addition rule. Because the event drawing a heart is not mutually exclusive from the event drawing a Jack, we must subtract the probability of getting both. Otherwise, we will double-count the Jack of Hearts.

First, find the probability of each event occuring

Now, find the probability of drawing both a Jack and a Heart. There is one card that is both.

Now, solve the equation.

### Example Question #14 : How To Use The Addition Rule

You have a deck of cards and you draw one card.  What is the probability of drawing an ace or a spade?

Explanation:

You must use the addition rule of probability which is the probability of either of two dependent events happening is the sum of the probabilities of each dependent event minus the probabilty of both happening (this eliminates double counting possible out comes).  The probabilty of getting an ace is  and the probability of getting a spade is .  The probability of getting an ace of spades is .  The final answer would then be =

### Example Question #15 : How To Use The Addition Rule

Billy likes to play sports. He plays baseball 30% of his afternoons, and soccer 40%. But he gets tired so he only plays both sports in the same day 15% of the time.

How many days a week does Billy play sports? (with rounding)

Explanation:

Billy plays baseball 40%+football 30% gets 70%.

But he plays both 15% so:

%

### Example Question #14 : Probability

If  and  , what is ?

Explanation:

2 ways: 1st, sum of , since  anything above 1 represents the overlap, or

2nd: since , the portion of the data in B and not A () is  (think venn diagram), and thus the portion of  included in A is