Download SOL 6.16 Probability

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)

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?
1
1
1
P(blue and red) = P(blue)  P(red after blue) = 3 × 2 = 6
SOL 6.16 Probability
Ex: When rolling two number cubes simultaneously, what is the probability
of rolling a 3 on one cube and a 4 on the other?
1
1
1
P(3 and 4) = P(3)  P(4) = 6 × 6 = 36
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Vocabulary:
Probability
A
B
A
A
C
B
C
P(A) =
3
7
unlikely
0
impossible
likely
3
7
1
1
2
certain
Probability of Independent Events
P(green) =
SOL 6.16 Probability
2
197
3
8
P(yellow) = =
8
1
4
P(green and yellow) =
3 1
P(green) ∙ P(yellow) = ∙ =
8 4
3
32
Probability of Dependent 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?
P(red) ∙ P(green after red) =
4
2
8
2
×
=
=
12 11 132 33
Candy Jar
G
P
R B R
Y
G
P
R B R
Y
Essential Understandings:
How can you determine if a situation involves dependent or independent events?
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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.
SOL 6.16 Probability
Essential Knowledge & Skills:
198
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?
SOL 6.16 Probability
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?
199