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### Probability

### Probability

### Probability

Data, Stats, and Probability

Probability

Impossible

Possible but not certain

Certain

Probability 0

Probability between 0 and 1

Probability 1

What are some events that have a probability of 1?

What are some events that have a probability of 0?

Probability

The probability that an event will happen is given by the following formula:

number of favorable outcomes

P (event) =

total number of outcomes

Probability

A bag contains the following:

7 red marbles

6 green marbles

7 white marbles

What is the probability of selecting a red marble?

7 red marbles

7

number of favorable outcomes

P (red) =

=

20 total marbles

total number of outcomes

20

Probability

Two numbered cubes are rolled. What is the probability that the sum of their numbers will be equal to 7?

6

1

P(7)=

=

How can their sum equal 7?

36

6

1 and 6

2 and 5

3 and 4

6 and 1

5 and 2

4 and 3

How many total outcomes are there when you roll two numbered cubes?

6 for Cube 1

6 for Cube 2

= 36 total

Probability

For the pair of spinners below, draw a tree diagram showing the outcomes when spinner 1 is spun and spinner 2 is spun.

1

2

1

2

3

4

3

Probability

1

2

1

2

3

4

3

If both spinners are spun, what is the probability that the sum will equal 5?

P (sum equals 5) =

Probability

If the probability of an event is 0, then:

It is certain

It is impossible

It is probable but not certain

It is probable but not impossible

Data, Stats, and Probability

Probability

If you flip a coin, what is the probability that it lands on either heads or tails?

This is an example of an “or” statement

Probability

“Or” statements:

An “or” statement will increase the number of favorable outcomes without increasing the total number of outcomes

→ increases the probability of an event

Probability

Suppose you roll a pair of numbered cubes. What is the probability that the two numbers are equal or their sum equals 7?

Sum = 7

Equal:

6 and 1

12

1 and 1

Prob. =

2 and 2

1 and 6

36

3 and 3

2 and 5

1

=

4 and 4

5 and 2

3

5 and 5

3 and 4

4 and 3

6 and 6

Probability

Suppose you select a card at random from a standard deck of cards. Find the probability that it is:

1

P (ace of spades) =

52

13

1

P (heart) =

=

52

4

14

7

=

P (heart or ace of spades) =

52

26

Data, Stats, and Probability

Probability

- Probability of multiple events
- If you flip a coin, what is the probability that the coin will land on heads?
- If you flip the coin again, what is the probability that it will land on heads again?
- What is the probability of flipping a coin twice and having it land on heads twice?

Probability

When you are finding the probability of multiple events:

Find the probability of each event separately

Multiply the two probabilities together

Reduce to lowest terms

Probability

You flip a coin and roll a numbered cube. What is the probability of the coin landing on tails and the numbered cube landing on 4?

P (tails) =

P (4) =

P (tails & 4) =

Probability

You pick two cards at random from a standard deck of cards without replacing them. What is the probability that you pick a red card followed by a black card?

P (red) =

P (black) =

P (red, black) =

Probability

A deck of cards has 4 orange, 5 pink, and 5 yellow cards. You pick 3 cards from the deck. Cards are not returned to the deck after they are picked. What is the probability the first card is yellow, the second card is pink, and the third card is orange?

P (y.) =

P (p.) =

P (o.) =

P (y,p,o) =

Probability

Classwork / homework if you do not finish:

Worksheet on probability of single and multiple events.

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