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 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. 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. 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 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 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. 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) 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. 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 . Problem How many 3-digit numbers can be formed from the digits 1, 2 and 3 if repetition of digits is not allowed? 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 The fundamental principle of counting provides a rule in determining the number of chance occurrence of events. This is known as the multiplication rule . 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.  #### You've reached the end of your free preview.

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• Fall '17
• Antonino Magallen

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