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The key concepts of probability and probability distribution from chapter 4 of ma 120. It covers the definition of probability, useful counting rules, and event composition and relations. Examples and formulas for calculating probabilities and the number of ways to arrange or choose events.
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Chapter 4 - Probability and Probability distribution
Example 1) When tossing a die once, what is the probability to get odd number(s)?
experiment: toss a die and observe the number that appears on the upper face event: observe an odd number = {1,3,5} sample space(S) = the set of all simple events={1,2,3,4,5,6} probability of the event = numbers in the event numbers in the sample space
Note: (a) Each probability must lie between 0 and 1. (b) Probability of the sample space = P (S) = 1
(b) P (^) rn = n! (n − r)! (number of ways we can arrange r out of n)
Example 3) P 23 =
(c) Crn = n! r!(n − r)! (number of ways we can choose r out of n)
Example 4) C 23 =
(b) A ∪ B
(c) A ∩ B
(d) P (A ∪ B)
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