Probability and Contingency Tables

Contingency table Suppose that we have two variables, gender (male or female) and right or left handedness. Population sampled = 100 How can we write the results in a way that helps us display the data? Data distribution can be written in a contingency table Right Handed Left Handed Totals Males 43 9 52 Females 44 4 48 TOTALS 87 13 100

Gender and L or R handed Right Handed Left Handed Totals Males 43 9 52 Females 44 4 48 TOTALS 87 13 100 What is the probability one of the participants is a female? (# females/Total) What is the probability someone is left handed ? (total left hand/ total) What is the probability someone is a left handed male? (# of left handed males / total)

Gender and L or R handed Right Handed Left Handed Totals Males 43 9 52 Females 44 4 48 TOTALS 87 13 100 Conditional probability gives you a “condition” and then asks for a probability What is the probability the participant is male knowing that they are left handed ? (# males that are left handed / total left hands = 9/13)

Gender and L or R handed Right Handed Left Handed Totals Males 43 9 52 Females 44 4 48 TOTALS 87 13 100 What is the probability someone is right handed knowing they are female? (# of female right hands / total females = 44/48) What is the probability someone is female knowing they are right handed? (# of right handed females/total right handed = 44/87)

Probability P(A) = part/whole A = male wearing green P(A) = 2/15 B = wearing red P(B) given they are women 4/10

Probability P(A) = part/whole C = they are wearing red If they are all men, what is P(C)? D = they are women Gven they are wearing green, what is the P(D)?

How to complete a contingency table Total All outcomes

Use the subtotals and information given Subtotal of 1rst row Subtotal of 2nd row Subtotal of 1rst column Subtotal of 2nd column All outcomes

Use the subtotals and information given Black Red Total Bugetti veron 7 3 Subtotal of 1rst row 10 Ferrari 5 35 Subtotal of 2nd row 40 Subtotal of 1rst column 12 Subtotal of 2nd column 38 All outcomes 50

Conditional Probability P(A | B) : A and B are two events, the conditional probability that A occurs given that B already has “P(A | B)”

A frog climbing out of a well is affected by the weather. When it rains, he falls back down the well with a probability of 1/10. In dry weather, he only falls back down with probability of 1/25. The probability of rain is 1/5 (therefore the probability it won’t raing is 4/5).

Complimentary events A and A (A + A = 1) - - Events are complimentary when their probability adds up to one They complement each other meaning if one doesn’t happen the other will. Example: There are 30 skittles (of course!) 10 red, 10 yellow, 10 green Event A is getting a green P(A) = 10/30 or 1/3 Event A is not getting green P(A) = 20/30 or 2/3 _ -

Example: Will the Frog Fall? - - The probability of rain is 1/5 P(R) = 1/5 Therefore: the probability it won’t rain is 4/5 P(R) = 4/5 P of falling when it rained is 1/10 The P of not falling when it rained is 9/10 The P of falling when it’s dry is 1/25 The P of not falling when it’s dry is 24/25 _

Event R = it rains Event F = the frog falls P( it rains and he falls) P (rains and he doesn’t fall) P(doesn’t rain and he falls P( it doesn’t rain and he doesn’t fall