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Algebra 1 Notes: Probability Part 3: Compound Probability

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Objectives Find the probability of compound events Identify which events are dependent and independent Identify which events are mutually exclusive and mutually inclusive Find the probability of mutually inclusive and mutually exclusive events

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Vocabulary Simple Event One event occurs. We did this already.

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Compound Probability The probability of two events occurring is the product of the probability of A and the probability of B. P(A and B) = P(A) P(B)

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Vocabulary Independent Events The first event does NOT effect the second event Dependent Events The first event DOES effect the second event

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Example 1 A bin contains 8 blue chips, 5 red chips, 6 green chips, and 2 yellow chips. Find each probability. a) Drawing a red chip, replacing it, then drawing a green chip Independent P(red, green) =

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Example 1 A bin contains 8 blue chips, 5 red chips, 6 green chips, and 2 yellow chips. Find each probability. a) Drawing a red chip, replacing it, then drawing a green chip Independent P(red, green) =

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Example 1 A bin contains 8 blue chips, 5 red chips, 6 green chips, and 2 yellow chips. Find each probability. a) Drawing a red chip, replacing it, then drawing a green chip Independent P(red, green) = =

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Example 1 A bin contains 8 blue chips, 5 red chips, 6 green chips, and 2 yellow chips. Find each probability. b) Selecting two yellow chips without replacement. Dependent P(yellow, yellow) =

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Example 1 A bin contains 8 blue chips, 5 red chips, 6 green chips, and 2 yellow chips. Find each probability. b) Selecting two yellow chips without replacement. Dependent P(yellow, yellow) =

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Example 1 A bin contains 8 blue chips, 5 red chips, 6 green chips, and 2 yellow chips. Find each probability. b) Selecting two yellow chips without replacement. Dependent P(yellow, yellow) = =

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Example 1 A bin contains 8 blue chips, 5 red chips, 6 green chips, and 2 yellow chips. Find each probability. c) Choosing green, then blue, then red, replacing each chip after it is drawn. Independent P(green, blue, red) =

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Example 1 A bin contains 8 blue chips, 5 red chips, 6 green chips, and 2 yellow chips. Find each probability. c) Choosing green, then blue, then red, replacing each chip after it is drawn. Independent P(green, blue, red) =

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Example 1 A bin contains 8 blue chips, 5 red chips, 6 green chips, and 2 yellow chips. Find each probability. c) Choosing green, then blue, then red, replacing each chip after it is drawn. Independent P(green, blue, red) =

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Example 1 A bin contains 8 blue chips, 5 red chips, 6 green chips, and 2 yellow chips. Find each probability. c) Choosing green, then blue, then red, replacing each chip after it is drawn. Independent P(green, blue, red) = =

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Example 1 A bin contains 8 blue chips, 5 red chips, 6 green chips, and 2 yellow chips. Find each probability. d) Choosing green, then blue, then red, without replacing each chip. Dependent P(green, blue, red) =

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Example 1 A bin contains 8 blue chips, 5 red chips, 6 green chips, and 2 yellow chips. Find each probability. d) Choosing green, then blue, then red, without replacing each chip. Dependent P(green, blue, red) =

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Example 1 A bin contains 8 blue chips, 5 red chips, 6 green chips, and 2 yellow chips. Find each probability. d) Choosing green, then blue, then red, without replacing each chip. Dependent P(green, blue, red) =

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Example 1 A bin contains 8 blue chips, 5 red chips, 6 green chips, and 2 yellow chips. Find each probability. d) Choosing green, then blue, then red, without replacing each chip. Dependent P(green, blue, red) = =

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Complements A complement is one of two parts that make up a whole (Probability of one). P(green) P(not green) sum of probabilities

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Mutually Exclusive If two events, A and B, are mutually exclusive, then the probability that either A or B occurs is the sum of their probabilities. We did these already too. P(A or B) = P(A) + P(B)

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Example 2 Alfred is going to the Lakeshore Animal Shelter to pick a new pet. Today, the shelter has 8 dogs, 7 cats, and 5 rabbits available for adoption. If Alfred randomly picks an animal to adopt, what is the probability that the animal would be a cat or a dog? P(cat or dog)

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Example 2 Alfred is going to the Lakeshore Animal Shelter to pick a new pet. Today, the shelter has 8 dogs, 7 cats, and 5 rabbits available for adoption. If Alfred randomly picks an animal to adopt, what is the probability that the animal would be a cat or a dog? P(cat or dog) = P(cat) + P(dog) =

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Example 2 Alfred is going to the Lakeshore Animal Shelter to pick a new pet. Today, the shelter has 8 dogs, 7 cats, and 5 rabbits available for adoption. If Alfred randomly picks an animal to adopt, what is the probability that the animal would be a cat or a dog? P(cat or dog) = P(cat) + P(dog) = +

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Example 2 Alfred is going to the Lakeshore Animal Shelter to pick a new pet. Today, the shelter has 8 dogs, 7 cats, and 5 rabbits available for adoption. If Alfred randomly picks an animal to adopt, what is the probability that the animal would be a cat or a dog? P(cat or dog) = P(cat) + P(dog) = + =

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Example 2 Alfred is going to the Lakeshore Animal Shelter to pick a new pet. Today, the shelter has 8 dogs, 7 cats, and 5 rabbits available for adoption. If Alfred randomly picks an animal to adopt, what is the probability that the animal would be a cat or a dog? P(cat or dog) = P(cat) + P(dog) = + = =

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Inclusive -overlap If two events, A and B, are inclusive, then the probability that either A or B occurs is the sum of their probabilities decreased by the probability of both occurring. P(A or B) = P(A) + P(B) – P(A and B)

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Example 3 A dog has just given birth to a litter of 9 puppies. There are 3 brown females, 2 brown males, 1 mixed- color female, and 3 mixed-color males. If you choose a puppy at random from the litter, what is the probability that the puppy will be male or mixed color? P(male or mixed color) =

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Example 3 A dog has just given birth to a litter of 9 puppies. There are 3 brown females, 2 brown males, 1 mixed- color female, and 3 mixed-color males. If you choose a puppy at random from the litter, what is the probability that the puppy will be male or mixed color? P(male or mixed color) = = P(male) + P(mixed color) – P(male and mixed color) =

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Example 3 A dog has just given birth to a litter of 9 puppies. There are 3 brown females, 2 brown males, 1 mixed- color female, and 3 mixed-color males. If you choose a puppy at random from the litter, what is the probability that the puppy will be male or mixed color? P(male or mixed color) = = P(male) + P(mixed color) – P(male and mixed color) = +

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Example 3 A dog has just given birth to a litter of 9 puppies. There are 3 brown females, 2 brown males, 1 mixed- color female, and 3 mixed-color males. If you choose a puppy at random from the litter, what is the probability that the puppy will be male or mixed color? P(male or mixed color) = = P(male) + P(mixed color) – P(male and mixed color) = + –

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Example 3 A dog has just given birth to a litter of 9 puppies. There are 3 brown females, 2 brown males, 1 mixed- color female, and 3 mixed-color males. If you choose a puppy at random from the litter, what is the probability that the puppy will be male or mixed color? P(male or mixed color) = = P(male) + P(mixed color) – P(male and mixed color) = + – =

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Example 3 A dog has just given birth to a litter of 9 puppies. There are 3 brown females, 2 brown males, 1 mixed- color female, and 3 mixed-color males. If you choose a puppy at random from the litter, what is the probability that the puppy will be male or mixed color? P(male or mixed color) = = P(male) + P(mixed color) – P(male and mixed color) = + – = =

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Homework Worksheet: Compound Probability

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