handout_4_2 - 4.2 Probability Models probability model a...

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4.2 Probability Models probability model - a description of a random phenomenon in the language of mathematics description of coin tossing has two parts: a list of possible outcomes a probability for each outcome The sample space S of a random phenomenon is the set of all possible outcomes. random phenomenon- toss a coin S= {H, T} random phenomenon- let your pencil fall blindly into Table B of random digits S= {0, 1, 2, 3, 4, 5 ,6, 7, 8, 9} random phenomenon- toss a coin four times and record the results vague- what constitutes an outcome? random phenomenon- toss a coin four times and record the results of each of 4 tosses in order S= {HHHH, HHHT, HHTH, HTHH, THHH…} 16 possibilities random phenomenon- toss a coin four times and count the number of heads S= {0, 1, 2, 3, 4} random phenomenon- computer generates random number between 0 and 1 S= {all numbers between 0 and 1} event - an outcome or a set of outcomes of a random phenomenon (an event is a subset of the sample space) random phenomenon- toss a coin four times and record the results of each of 4 tosses in order event A= “get exactly 2 heads” event A expressed as a set of outcomes: A= {HHTT, HTHT, HTTH, THHT, THTH, TTHH}
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Probability Rules 1) Any probability is a number between 0 and 1. The probability P(A) of any event A satisfies 0 P(A) 1. 2) All possible outcomes together must have probability 1. If S is the sample space in a probability model, then P(S) = 1. 3) If two events have no outcomes in common, the probability that one or the other occurs is the sum of their individual probabilities. Two events A and B are disjoint if they have no outcomes in common and so can never occur together. If A and B are disjoint, P(A or B) = P(A) + P(B) This is the addition rule for disjoint events . EX) random phenomenon- toss a coin once (A-heads, B- tails) A and B disjoint- no outcomes in common (can’t get heads and tails at same time) P (H or T) = P (H) + P (T) 0.5 + 0.5 = 1 EX) random phenomenon- toss a die (A-1, B- odd #) A and B not disjoint- have outcome in common (roll a 1) P (A or B) P(A) + P(B) 4) The probability that an event does not occur is 1 minus the probability that the event does occur.
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