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Probability and Contingency Tables

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?

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Probability and Contingency Tables

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  1. Probability and Contingency Tables

  2. 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

  3. Genderand L or R handed 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)

  4. Genderand L or R handed 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)

  5. Genderand L or R handed 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)

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

  7. ProbabilityP(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)?

  8. How to complete a contingency table

  9. Use the subtotals and information given

  10. Use the subtotals and information given

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

  12. What is the probability that the car is a Ferrari, given that it is black?

  13. What is the probability that the car is black given that it is a Bugetti Veron?

  14. 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 rain is 4/5).

  15. Complimentary eventsA 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

  16. 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

  17. Event R = it rainsEvent 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

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