12.5 Compound probability

Compound Probability

Objectives

Learning Objectives: Students will identify independent and dependent probability and determine the probability of compound events.

Language Objective: Students will express their reasoning in written form.

Vocabulary

A compound probability is a probability involving two or more events, for example, the probability of Event A and Event B happening.

For example the compound probability may be like the following:

A. What’s the probability of flipping a coin twice and having it come up heads both times?

B. P(Comes up heads) =

C. P(1^st flip comes up heads AND 2^nd flip comes up heads) =

Vocabulary

Independent Probability: The outcome of one event does not effect the outcome of the other event. *Look for words like: replace, replacement, put back*

Example: Rolling a six-sided die and spinning a spinner.

Vocabulary

Dependent Probability: The outcome of one event affects the outcome of the other event. *Look for words like: without replacement, at the same time, or one afer another.*

Example: Suppose two M&M’s are drawn from the bag above. The first M&M is not replaced before the second M&M is drawn.  

Example 1

Tell whether the events are dependent or independent.

A) One tossed coin landing heads and the next landing tails.

B) Drawing two cards from a deck of cards at the same time.

Multiple Choice

Tell whether the events are dependent or independent.

Rolling two sixes in a row on a number cube.

• Independent

• Dependent

Multiple Choice

Tell whether the events are dependent or independent.

Drawing a blue tile from a bag and then drawing a red tile without replacing the first tile.

• Independent

• Dependent

Multiplication Rule

The probability that Events A and B both occur is equal to the probability that Event A occurs times the probability that Event B occurs, given that A has occurred.

Formula: Independent Event (with replacement)

Multiple Choice

A bag contains 4 blue marbles, 6 green marbles and 3 yellow marbles. If two marbles are drawn at random from the bag.

What’s the probability of drawing a green marble, replacing it, and then drawing a yellow marble?

• 
  

  $$\frac{9}{13}$$

• $$\frac{54}{13}$$

• $$\frac{9}{169}$$

• $$\frac{18}{169}$$

Formula: Dependent Event (without replacement)

Multiple Choice

A bag contains 4 blue marbles, 6 green marbles and 3 yellow marbles. If two marbles are drawn at random from the bag.

What’s the probability of drawing a green marble, without replacing it, and then drawing a yellow marble?

• $$\frac{3}{25}$$

• $$\frac{9}{25}$$

• $$\frac{3}{26}$$

• $$\frac{9}{26}$$