4-probability.ppt - Topic 4 PROBABILITY Sample Space Fundamental Principle of Counting Permutations Combinations Probability of an Event Additive Rules

4-probability.ppt - Topic 4 PROBABILITY Sample Space...

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Topic 4. Sample Space Fundamental Principle of Counting Permutations Combinations Probability of an Event Additive Rules Conditional Probability Bayes’ Rule PROBABILITY
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Objectives Count efficiently by applying the Fundamental Principle of Counting Count using permutation and combination. Determine the probability of a given event. Apply the different laws of probability. Interpret probability values.
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Probability - a specific term is a measure of the likelihood that a particular event will occur. Low Probability - rare or unusual occurrences Event – a collection of outcome of a procedure. Outcome we’re looking for. Simple Event – a single outcome or one specific outcome we get from procedure. Sample Space – all simple events or every possible outcome.
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Example Procedure Simple Event Sample Space Flip coin one time Head Head or Tail Flip coin 3 times 1 head, and 2 tails H, H, H or T,T,T HHT, HTH,HTT,TTH,THT,THH
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Probability - the likelihood of an event occurring, P. P(A) – probability of event A happening. 3 Type of Probability: 1.Observed Probability - probability that is estimated based on observation. “What did happen?” P(A) = # of times A occurred divided by # of times procedure was repeated
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2. Classical Probability – probability based on the chance of an even occurring. (Each simple event must have an equal chance of occurring.) “What should happen”. Comes from “priori”, a latin word means “before”. P(A) = # of way could occur divided by # of simple events (outcomes) 3. Subjective Probability – an educated guess.
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Example: 1.The probability of selecting a heart from a deck of cards. P(H) = 13/52 = 0.25 (Classical – what should happen) 2. Flip coin 100 times, you get 64 tails. P(T) = 64/100 = 0.64 (Observed-what did happen) 3. Peyton completed 385 out of his first 528 passes. Find the probability that Peyton will complete a pass. P(Complete a pass) = 385/528 = 0.729 0r 72.9% (observed)
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4.) 260 bolts are examined as they are produced. Five of them are found to be defective. On the basis of this information, estimate the probability that a bolt will be defective. P(B) = 5 / 260 = 0.019.
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Knowledge of counting the number of ways by which events can happen is important in the study of probability. The elements of a sample space can be systematically listed by means of a tree diagram .
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Problem How many 3-digit numbers can be formed from the digits 1, 2 and 3 if repetition of digits is not allowed?
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Solution: Hundredth Digit Tenth Digit Unit Digit Number 1 2 3 2 3 3 2 123 132 1 3 3 1 1 2 2 1 213 231 312 321 Answer: 6 numbers
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The fundamental principle of counting provides a rule in determining the number of chance occurrence of events. This is known as the multiplication rule .
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If one thing can be done in n 1 ways and a second thing can be done in n 2 ways, then the sequence of things can be done together in n 1 n 2 ways.
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  • Fall '17
  • Antonino Magallen

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