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Warm Up

Material Taken From: Mathematics for the international student Mathematical Studies SL Mal Coad , Glen Whiffen , John Owen, Robert Haese , Sandra Haese and Mark Bruce Haese and Haese Publications, 2004. Warm Up.

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Warm Up

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  1. Material Taken From:Mathematicsfor the international student Mathematical Studies SLMal Coad, Glen Whiffen, John Owen, Robert Haese, Sandra Haese and Mark BruceHaese and Haese Publications, 2004

  2. Warm Up • In a group of 108 people in an art gallery 60 liked the pictures, 53 liked the sculpture and 10 liked neither. • What is the probability that a person chosen at random liked the pictures but not the sculpture?

  3. Section 14K – Laws of Probability • BrainPop Video • Compound Events Today: • Sometimes events can happen at the same time. • Sometimes you will be finding the probability of • event A or event B happening. • Sometimes you will be finding the probability of • event A and event B happening.

  4. Laws of Probability

  5. Mutually Exclusive Events • A bag of candy contains 12 red candies and 8 yellow candies. • Can you select one candy that is both red and yellow?

  6. Laws of Probability

  7. Mutually Exclusive Events P(either A or B) = P(A) + P(B)

  8. Example 1)Of the 31 people on a bus tour, 7 were born in Scotland and 5 were born in Wales. • Are these events mutually exclusive? • If a person is chosen at random, find the probability that he or she was born in: • Scotland • Wales • Scotland or Wales

  9. Laws of Probability

  10. Combined Events P(either A or B) = P(A) + P(B) – P(A and B)

  11. Example 2)100 people were surveyed: • 72 people have had a beach holiday • 16 have had a skiing holiday • 12 have had both What is the probability that a person chosen has had a beach holiday or a ski holiday?

  12. Example 3)If P(A) = 0.6 and P(A  B) = 0.7 andP(A  B) = 0.3, find P(B).

  13. Conditional ProbabilityTen children played two tennis matches each. What is the probability that a child won his first match, if it is known that he won his second match?

  14. Laws of Probability

  15. Example 4) In a class of 25 students, 14 like pizza and 16 like iced coffee. One student likes neither and 6 students like both. One student is randomly selected from the class. What is the probability that the student: • likes pizza • likes pizza given that he/she likes iced coffee?

  16. Example 5) In a class of 40, 34 like bananas, 22 like pineapples and 2 dislike both fruits. If a student is randomly selected find the probability that the student: • Likes both fruits • Likes bananas given that he/she likes pineapples • Dislikes pineapples given that he/she likes bananas

  17. Example 6)The top shelf of a cupboard contains 3 cans of pumpkin soup and 2 cans of chicken soup. The bottom self contains 4 cans of pumpkin soup and 1 can of chicken soup. Lukas is twice as likely to take a can from the bottom shelf as he is from the top shelf . If he takes one can without looking at the label, determine the probability that it: • is chicken • was taken from the top shelf given that it is chicken

  18. Section 14L – Independent Events Independent Events • If one student in the class was born on June 1st can another student also be born on June 1st? • If you roll a die and get a 6, can you flip a coin and get tails?

  19. Laws of Probability

  20. Example 7) P (A) = ½ P (B) = 1/3 and P(A  B) = p Find p if: A and B are mutually exclusive A and B are independent

  21. Homework • Worksheet: • 16I.1 #1-4 all • 16I.2 #1, 3, 5, 6, 7 • 16J

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