Warm Up One card is drawn from the deck. Find each probability.

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Warm Up One card is drawn from the deck. Find each probability. 1. selecting a two 2. selecting a face card Two cards are drawn from the deck. Find each probability. 3. selecting two kings when the first card is replaced. 4. selecting two hearts when the first card is not replaced.

Objectives Vocabulary Find the probability of mutually exclusive events. Find the probability of inclusive events. Vocabulary simple event compound event mutually exclusive events inclusive events

A simple event is an event that describes a single outcome A simple event is an event that describes a single outcome. A compound event is an event made up of two or more simple events. Mutually exclusive events are events that cannot both occur in the same trial of an experiment. Rolling a 1 and rolling a 2 on the same roll of a number cube are mutually exclusive events.

Example 1: Finding Probabilities of Mutually Exclusive Events A group of students is donating blood during a blood drive. A student has a probability of having type O blood and a probability of having type A blood. Explain why the events “type O” and “type A” blood are mutually exclusive. What is the probability that a student has type O or type A blood?

Inclusive events are events that have one or more outcomes in common. When you roll a number cube, the outcomes “rolling an even number” and “rolling a prime number” are not mutually exclusive. The number 2 is both prime and even, so the events are inclusive.

Example 2A: Finding Probabilities of Compound Events Find the probability on a number cube. rolling a 4 or an even number rolling an odd number or a number greater than 2

Example 3: Application Of 1560 students surveyed, 840 were seniors and 630 read a daily paper. The rest of the students were juniors. Only 215 of the paper readers were juniors. What is the probability that a student was a senior or read a daily paper?

Example 4 Application Each of 6 students randomly chooses a butterfly from a list of 8 types. What is the probability that at least 2 students choose the same butterfly? P(at least 2 students choose same) = 1 – P(all choose different) Use the complement.