# 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.

Bloom's Level:  Analyze, Evaluate

### BIG IDEAS

• I can predict my chances of winning a raffle, determine the Heisman trophy winner, and foretell what flavor gumball will come out of the machine next.
• I will understand that the likelihood of an event occurring can be described numerically and used to make predictions.

### 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.
• A probability of 0 means the event will never occur.
• 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).
• 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

### ESSENTIALS

• How can you determine if a situation involves dependent or independent events?  Events are independent when the outcome of one has no effect on the outcome of the other. Events are dependent when the outcome of one event is influenced by the outcome of the other.

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

6.16a1 Determine whether 2 events are dependent or independent.

6.16a2  Compare and contrast dependent and independent events.

6.16b1  Determine the probability of 2 dependent events.

6.16b2  Determine the probability of 2 independent events.

### KEY VOCABULARY

probability, dependent event, independent event, simple event, simultaneously, outcome

Updated: Jun 06, 2017