Probability of Compound Events

Section 12-7

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Compound Event

The joint probability of 2 or more events.

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Example: A bag contains 6 black marbles and 4 blue marbles. What is the probability of drawing black, replacing it then drawing blue.

Independent Events

A compound event where the outcome of one event does not affect the outcome of the other

Finding Probability of Independent Events

Multiply the probabilities of the two events.

Example: P(black) • P(Blue)

Dependent Events

Events where the outcome of one event affects the outcome of the next.

Example: What is the probability of drawing two kings from a deck of cards?

Finding Probability of Dependent Events

Find the probability of the first event, then find probability of second event after the first happened.

Multiply the two probabilities.

Dependent Example

What is the probability of drawing two kings from a deck of cards?

P(King and King) = P(First King) • P(Second King)

P(King and King) = 4/52 • 3/51

Mutually Exclusive Events

Events that cannot occur at the same time.

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Example: What is the probability of rolling a die and getting a 2 or a 4.

Probability of Mutually Exclusive Events

Add the probabilities of the two events.

P(A or B) = P(A) + P(B)

Example: Probability of rolling a 2 or a 4

P(2 or 4) = P(2) + P(4)

P(2 or 4) = ⅙ + ⅙

Probability of Events That Are Not Mutually Exclusive

Example: 10 girls were surveyed. 8 were on the honor roll and 6 played soccer. What is the probability that a girl selected randomly was on the honor roll or played soccer?

Formula: P(soccer or honor roll) = P(soccer) + P(honor roll) - P(both)

Venn Diagrams for Compound Probability

How many students were

surveyed?

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Example 2:

What is the probability that a

students doesn’t take any of

these classes?