Probability and Simulation CONDITIONAL PROBABILITY

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 P [A or B] P [A] =

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

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

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.

Warm - up Ilse wins Nick wins TOTAL Less than 10-mins4913 more than 10-mins527 Total91120 P [ Ilse winning ] P [ Ilse NOT winning ] P [ less than 10 mins. warm up ] P [ more than 10 mins. warm up ] = 9/20 =.45 = =.55 = 13/20 =.65 = 7/20 =.35

Warm - up Ilse wins Nick wins TOTAL Less than 10-mins4913 more than 10-mins527 Total91120 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 = 71% Ilse has more chances of winning if they have more warm up time

Example 2: NondefectiveDefectiveTOTAL Company Company Total18725 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 P [ A ] = P [ B ] = P [A | B] = 5/25 =.20 = 5/7 =.714 P [A|B] = P[company 1 | defective] Buying a blowdryer from Wallmart

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: Have been personally criticized Have NOT been personally criticized Total Have criticized others Have NOT criticized others Total C = event that the individual has criticized others O = event that the individual has been personally criticized by others

OO CC Have been personally criticized Have NOT been personally criticized Total Have criticized others Have NOT criticized others Total P[C] = 27/193 =.1399 P[O] = 42/193 =.2176 P[C ∩ O] = 19/193 =.0984