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Probability and Simulation

Probability and Simulation. CONDITIONAL PROBABILITY. P [A or B]. =. P [A]. Conditional Probability. Defined as the probability of Event A knowing that Event B has already occurred. Notation:. P [ A | B ]. Read as Probability of A “given” B.

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Probability and Simulation

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  1. Probability and Simulation • CONDITIONAL PROBABILITY

  2. P [A or B] = P [A] Conditional Probability Defined as the probability of Event A knowing that Event B has already occurred. Notation: P [ A | B ] Read as Probability of A “given” B

  3. Probability model for the ages of undergrad students taking online courses: What is the probability that the students we draw are not in the traditional undergraduate age? = 1-P(18-23) P(not 18-23) = 1 - 0.57 = 0.43 That is 57% of distance learners are between 18-23 and 43% are not in this age group.

  4. What is the probability drawing students from 30-39 group or 40-over group? P(30 years over) = P(30-39 years) + P(40 and over) = .14 + .12 = 0.26 That is 26% of undergraduates in distance learning courses are at least 30 years old.

  5. Nick decided to play tennis with Ilse for lack of better things to do. Ilse likes to have a nice long warm-up session at the start, where she hits the ball back and forth on the wall, while Nick’s idea of warm up is to bend at the waste and tie his sneakers and to adjust his shorts. Ilse thinks that lack of warm up affects her game and Nick thinks otherwise. Nick then thought of recording their outcomes for the last 20 matches to prove his point. Let’s see if Ilse has a valid claim.

  6. P [ Ilse winning ] P [ less than 10 mins. warm up ] P [ Ilse NOT winning ] P [ more than 10 mins. warm up ] = 13/20 = .65 = 9/20 = .45 = 1-.45 = .55 = 7/20 = .35

  7. P [ Ilse winning | warm-up is LESS than 10 minutes ] = 4/13 = 31% P [ Ilse winning | warm-up is MORE than 10 minutes ] = 5 / 7 Ilse has more chances of winning if they have more warm up time = 71%

  8. P [A|B] P [ A ] = = P[company 1 | defective] P [ B ] = P [A | B] Example 2: Buying a blowdryer from Wallmart A = event that a hairdryer you bought is from Company 1 B = event that a hairdryer you bought is Defective 15/25 = .60 7/25 = .28 = 5/7 = .714 = 5/25 = .20

  9. Communication Research Reports, [1998]: published an article about “flaming” (negative criticism to each other in a forum/chatrooms). Data from this study are reproduced here: C = event that the individual has criticized others O = event that the individual has been personally criticized by others

  10. O C P[C∩O] = 19/193 P[C] = 27/193 = .0984 = .1399 P[O] = 42/193 = .2176

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