135 Notes and answers Reg Geo.notebook
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May 18, 2016
Nov 152:22 PM
Find the probability of mutually exclusive events.
Find the probability of inclusive events.
Objectives
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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.
135 Notes and answers Reg Geo.notebook
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Recall that the union symbol ∪ means or.
Remember!
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Example 1A: 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.
A person can only have one blood type.
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May 18, 2016
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Example 1B: Finding Probabilities of Mutually Exclusive Events
What is the probability that a student has type O or type A blood?
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.
P(type O ∪ type A) = P(type O) + P(type A)
Nov 152:22 PM
Check It Out! Example 1a
Each student cast one vote for senior class president. Of the students, 25% voted for Hunt, 20% for Kline, and 55% for Vila. A student from the Explain why the events “voted for Hunt,” “voted for Kline,” and “voted for Vila” are mutually exclusive.Each student can vote only once.
135 Notes and answers Reg Geo.notebook
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May 18, 2016
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Check It Out! Example 1b
What is the probability that a student voted for Kline or Vila?
Each student cast one vote for senior class president. Of the students, 25% voted for Hunt, 20% for Kline, and 55% for Vila. A student from the senior class is selected at random.
P(Kline ∪ Vila) = P(Kline) + P(Vila)= 20% + 55% = 75%
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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.
135 Notes and answers Reg Geo.notebook
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May 18, 2016
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There are 3 ways to roll an even number, {2, 4, 6}.
There are 3 ways to roll a prime number, {2, 3, 5}.
The outcome “2” is counted twice when outcomes are added (3 + 3) . The actual number of ways to roll an even number or a prime is 3 + 3 – 1 = 5. The concept of subtracting the outcomes that are counted twice leads to the following probability formula.
Recall that the intersection symbol ∩ means “and.”
Remember!
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Example 2A: Finding Probabilities of Compound Events
Find the probability on a number cube.
rolling a 4 or an even number
P(4 or even) = P(4) + P(even) – P(4 and even)4 is also an even number.
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May 18, 2016
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Example 2B: Finding Probabilities of Compound Events
rolling an odd number or a number greater than 2
P(odd or >2) = P(odd) + P(>2) – P(odd and >2)
There are 2 outcomes where the number is odd and greater than 2.
Find the probability on a number cube.
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Check It Out! Example 2a
A card is drawn from a deck of 52. Find the probability of each.
drawing a king or a heart
P(king or heart) = P(king) + P(heart) – P(king and heart)
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May 18, 2016
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Check It Out! Example 2b
drawing a red card or a face card
P(red or face) = P(red) + P(face) – P(red and face)
A card is drawn from a deck of 52. Find the probability of each.
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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?
The probability that the student was a senior or read the daily paper is about 67.6%.
P(senior ∪ reads paper)
= P(senior) + P(reads paper) – P(senior ∩ reads paper)
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Assignment(p. 910) 36, 810, 1318
Nov 2211:33 AM