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Chapter 12 PROBABILITY

Chapter 12 PROBABILITY. REVIEW. Counting, Combinations, Permutations, Probability, Binomial Theorem. Fundamental Counting Principle. EXAMPLE: How many different 7 digit phone numbers are possible if the first digit cannot be 0 or 1?.

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Chapter 12 PROBABILITY

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  1. Chapter 12 PROBABILITY REVIEW Counting, Combinations, Permutations, Probability, Binomial Theorem

  2. Fundamental Counting Principle EXAMPLE: How many different 7 digit phone numbers are possible if the first digit cannot be 0 or 1? Two events: one occurs m ways and the other occurs n ways…They occur together mn ways

  3. PERMUTATIONS • An ORDERING of n objects: n! • Permutations of n objects taken r at a time • Permutations with repetition

  4. Example Questions • There are 8 movies you would like to see currently showing in theaters. In how many different ways can you see all 8 of the movies?

  5. Example Questions • There are 8 movies you would like to see currently showing in theaters. In how many ways can you choose a movie to see this Saturday and one to see this Sunday?

  6. Example Questions • Find the number of distinguishable permutations of the letters in POPPY

  7. Example Questions • Find the number of distinguishable permutations of the letters in WATERFALL

  8. COMBINATIONS • Selection of objects – NO ordering • EXAMPLE: How many 5-card hands are possible when using a standard deck?

  9. BINOMIAL THEOREM • Pascal’s Triangle – coefficients of the binomial expansion • Sum of the exponents in each term must add to the original power EXAMPLE: Expand (x-5)4

  10. Pascal’s Triangle Write Pascal’s Triangle to the ( )7 line:

  11. Example Questions • Expand (x - 5)3

  12. Example MC Questions • What is the coefficient of x5 in the expansion of (2x - 3)6?A) 6 B) -36 C) 192 D) -576 E) -1152

  13. PROBABILITY • Probability: • P(A or B) = P(A) + P(B) – P(A and B)P(A and B) = P(A) • P(B)Complement: P(A’) = 1 – P(A)

  14. Example MC Questions • You have 6 best friends, but only 4 cupcakes. In how many different orders can you give four of your six best friends cupcakes?A) 4 B) 12 C) 24D) 120 E) 360

  15. Example MC Questions • In how many ways can a 5 person committee be chosen from a group of 8 people?A) 15 B) 40C) 56 D) 336E) 6720

  16. Example MC Questions • Events A and B are independent, P(A)=0.9 and P(B)=0.4. What is P(A and B)?A) 0.4 B) 0.9C) 1.3 D) 0.36E) 3.6

  17. Example MC Questions • The table below shows the number of students that like mustard and ketchup with their food.What is the probability that students who eat hamburgers choose ketchup as their condiment?A) .2 B) 0.25 C) 0.28D) 0.4 E) 0.14

  18. Example MC Questions • What is the probability that in a family of 6 children exactly three are boys? Assume a boy and girl are equally likely to occur.A) 1/3 B) 1/2 C) 5/16D) 5/32 E) 5/64

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