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# Probability models & basic rules

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Basic Notation and Rules of Probability

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### Probability models & basic rules

1. 1. Probability Models • Probability Model – the description of some chance process that consists of two parts, a sample space S and a probability for each outcome. • Tossing a coin – we know there are 2 possible outcomes – We believe that each outcome has a probability of ½ • Sample space – a list of possible outcomes – Can be written using set notation S = { T, H }
2. 2. Probability Notation • Probability models allow us to find the probability of any collection of outcomes called an EVENT • An event is a collection of outcomes from some chance process. (subset of sample space S notated as A, B, or C) • P(A) denotes the probability that event A occurs
3. 3. Probability of Events • Event A, sum of dice = 5, find P(A) = • Event B, sum of dice not = 5, find P(B) = • P(B) = P(not A) • Notice that P(A) + P(B) = 1
4. 4. Probability of Events • Consider Event C = sum of dice = 6 • Probability of getting sum of 5 or 6? P(A or C) since these events have no outcomes in common… P(sum of 5 or sum of 6) = P(sum of 5) + P(sum of 6) • P(A or C) = P(A) + P(C)
5. 5. Basic Rules • Probability of any event is a number between 0&1 • All possible outcomes (options in a sample space) must have probabilities that sum 1 • IF all outcomes in a sample space are equally likely, the probability that event occurs can be found using a formula: P(A) = number of outcomes corresponding to event A total number of outcomes in sample space
6. 6. Basic Rules • Probability that an event does not occur is 1 – (the probability that the event does occur). – The event that is “not A” is the complement of A and is denoted by AC • If two events have no outcomes in common, the probability that one or the other occurs is the sum of their individual probabilities. – When 2 events have no outcomes in common, we refer to them as mutually exclusive or disjoint
7. 7. Basic Rules • For any event A, 0 ≤ P(A) ≤ 1 • If S is the sample space in a probability model, P(S) = 1 • In the case of equally likely outcomes: P(A) = number of outcomes corresponding to event A total number of outcomes in sample space • Complement rule: P(AC) = 1 – P(A) • Addition rule for mutually exclusive events: If A and B are mutually exclusive, P(A or B) = P(A) + P(B)
8. 8. Probability Models • Distance learning courses are rapidly gaining popularity among college students. Here is randomly selected undergraduate students who are taking a distance-learning course for credit, and their student ages: Age group (yr) 18 to 23 24 to 29 30 to 39 40 or over Probability 0.57 0.17 0.14 0.12 1. Show that this is a legitimate probability model. 2. Find the probability that the chose student is not in the traditional college age group (18-23 years). Pg. 303