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SOL

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SOL 6.16 – Probability

6.16 The student will a) compare and contrast dependent and independent events; and b) determine probabilities for dependent and independent events.

Understanding the Standard:

The probability of an event occurring is equal to the ratio of desired outcomes to the total number of possible outcomes (sample space).

The probability of an event occurring can be represented as a ratio or the equivalent fraction, decimal, or percent.

The probability of an event occurring is a ratio between 0 and 1. o A probability of 0 means the event will never occur. o A probability of 1 means the event will always occur.

A simple event is one event (e.g., pulling one sock out of a drawer and examining the probability of getting one color).

A compound event is more than one event, multiply the probability of each event.

Events are independent when the outcome of one has no effect on the outcome of the other. For example, rolling a number cube and flipping a coin are independent events.

The probability of two independent events is found by using the following

formula: P(A and B) = P(A) P(B)

Ex: When rolling two number cubes simultaneously, what is the probability of rolling a 3 on one cube and a 4 on the other?

P(3 and 4) = P(3) P(4) = 1

6×

1

6=

1

36

Events are dependent when the outcome of one event is influenced by the outcome of the other. For example, when drawing two marbles from a bag, not replacing the first after it is drawn affects the outcome of the second draw.

The probability of two dependent events is found by using the following formula:

P(A and B) = P(A) P(B after A)

Ex: You have a bag holding a blue ball, a red ball, and a yellow ball. What is the probability of picking a blue ball out of the bag on the first pick and then without replacing the blue ball in the bag, picking a red ball on the second pick?

P(blue and red) = P(blue) P(red after blue) = 1

3×

1

2=

1

6

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Vocabulary:

Probability

A B A B A C C

P(A) = 3

7

0 1

2 1

Probability of Independent Events

P(green) =

3

8

P(yellow) = 2

8 =

1

4

P(green and yellow) =

P(green) ∙ P(yellow) = 3

8∙1

4 =

3

32

impossible certain

unlikely likely

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Probability of Dependent Events

P(red) ∙ P(green after red) = 4

12×

2

11=

8

132=

2

33

Essential Understandings:

How can you determine if a situation involves dependent or independent events?

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Essential Knowledge & Skills:

The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

Determine whether two events are dependent or independent.

Compare and contrast dependent and independent events.

Determine the probability of two dependent events.

Determine the probability of two independent events.

What is the probability of getting a red jelly bean on first pick and then without replacing it, getting a green jelly bean on the second pick?

Candy Jar

R R

G

Y

P

B

R R

G

Y

P

B

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Practice:

1. This chart shows the three pairs of pants and four shirts that Bobby packed for a trip. Bobby will randomly select an outfit to wear. He can choose one pair of pants and one shirt. Using the chart, determine the probability that he will select a pair of blue jeans and the yellow shirt.

Pants Shirt Color

Blue Jeans Orange

Blue Jeans Yellow

Khakis Green

Red

2. Alexis has a deck of cards labeled as follows: 3 cards with a heart, 2 cards with a circle, 1 card with a flower, 1 card with a ball

a) What is the probability that she will randomly select a card with a

heart, replace it, and then select a card with a ball?

b) What is the probability that she will randomly select a card with a circle, NOT replace it, and then select a card with a circle?

Released SOL questions: