WARM UP 1. If two fair dice are tossed, what is the probability that the sum is a 2 or a 3? 2. three fair coins are tossed. What is the probability that not all the coins are heads? 3. What is the complement of question 2?

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WARM UP1. If two fair dice are tossed, what is
the probability that the sum is a 2 or a 3?2.
three fair coins are tossed. What is the
probability that not all the coins are heads?3.
What is the complement of question 2?
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• Read the top of pg.440
• Multiplication Counting Principle
• The number of ways to choose one element in A and
  one element from B is N(A) ? N(B)

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• Define Replacement
• EXAMPLE with replacement
• How many ways are there to answer a test having
  5 true-false questions?

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• EXAMPLE with replacement
• If you guess on each question and all are equally
  likely, what is the probability of answering all
  5 questions correctly?

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• SELECTIONS WITH REPLACEMENT
• If a set has n elements. There are nk possible
  arrangements of k elements in the set with
  repacement.

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• There are nk possible arrangements of k elements
  in the set with repacement.
• (size of the sample space)
• n represents the number of options
• k represents how many

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• EXAMPLE There are two parts to a math test.
• Part 1 has 25 questions with five options each.
• Part 2 has 15 questions with four options each.
• How many ways are there to answer the test?

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• SELECTIONS WITHOUT REPLACEMENT
• Sue wants to rank order her choice for five
  colleges, how many rankings can she make?
• Name 5 colleges.

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• SELECTIONS WITHOUT REPLACEMENT
• For n a positive integer, n factorial is the
  product of the positive integers from 1 to n.
• In symbols it is
• n! n?(n-1)?(n-2)... 3 ? 2 ? 1

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SELECTIONS WITHOUT REPLACEMENT Let S be a set
with n elements. Then there are n! possible
arrangements of the n elemetns without
replacement.
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PROBLEMS

• Page 4437,6
• Page 4439,5

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HOMEWORK

• Read section 7-3
• Worksheet 7-3