Algebra 1 Notes: Probability Part 3: Compound Probability

1. Algebra 1 Notes:Probability Part 3:Compound Probability

2. 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

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

4. 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)

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

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

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

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

9. 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) =

10. 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) = •

11. 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) = • =

12. 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) =

13. 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) = •

14. 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) = • •

15. 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) = • • =

16. 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) =

17. 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) = •

18. 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) = • •

19. 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) = • • =

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

21. 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)

22. 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)

23. 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) =

24. 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) = +

25. 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) = + =

26. 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) = + = =

27. 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)

28. 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) =

29. 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) =

30. 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) = +

31. 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) = + –

32. 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) = + – =

33. 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) = + – = =

34. Homework Worksheet: Compound Probability