How to use the addition rule

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AP Statistics › How to use the addition rule

Questions 1 - 10
1

Assume there is an election involving three parties: D, R, and I. The probability of D winning is .11, R winning is .78, and I winning is .11. What is the probability of D or R winning?

.89

.78

1

0

Explanation

Since all of the events are mutually exclusive (one of the parties must win), you can get the probability of either D or R winning by adding their probabilities.

Since the probability of D winning is .11 and R winning is .78, the probability of D or R winning is .89.

2

Students collected 150 cans for a food drive. There were 23 cans of corn, 48 cans of beans, and 12 cans of tomato sauce. If a student randomly selects one can to give away, what is the probability that the can will be either tomato sauce or beans?

Explanation

In this case, we want to know the probability of multiple, mutually exclusive possible outcomes. The possible outcomes are mutually exclusive because one can of food could not be both beans and tomato sauce. To determine the probability of the two possible outcomes, add them together and then find the least common denominator.

3

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.

4

At a business conference, one participant was selected to give a presentation. There were total participants. had business degrees and did not. were entrepreneurs and were not. of those with business degrees were entrepreneurs. What is the probability that the person selected will have a business degree or be an entrepreneur?

Explanation

We want to know the probability of multiple possible outcomes that are not mutually exclusive. To do this, we use the addition rule with one step that we would not use if the possible outcomes were mutually exclusive.

Add the probabilities of each possible outcome, subtract from that sum the number counted twice, then reduce the answer to the least common denominator. In our case, we are told that 2 of those who have a business degree are also entrepreneurs therefore we need to subtract to from the total to get the correct probability.

5

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

6

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.

7

150 students are athletes at the school. 65 play baseball, 15 play basketball, and 10 play both basketball and baseball.

What is the probability that a randomly selected athlete will play either baseball or basketball or both sports?

Explanation

We want to know the probability of multiple possible outcomes that are not mutually exclusive. To do this, we use the addition rule with one step that we would not use if the possible outcomes were mutually exclusive. Add the probabilities of each possible outcome, subtract from that sum the number counted twice, then reduce the answer to the least common denominator.

8

A student randomly selected a highlighter from her desk. There were five highlighters on the desk, each of a different color--blue, green, yellow, red, and orange. What is the probability that the student selected either the red or the yellow highlighter?

Explanation

In this case, we want to know the probability of multiple, mutually exclusive possible outcomes. To determine the probability of the two possible outcomes, simply add them together. This is called the addition rule.

9

If 1 card is chosen at random from a deck of cards, what is the probability that it will be a heart or a king?

4/13

26/52

17/52

13/52

29/52

Explanation

In a deck of cards, there are 52 total cards, 13 hearts, 4 kings, and 1 king that is a heart.

So,

10

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:

%

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