Probability and contingency tables
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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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Probability and contingency tables

Probability and Contingency Tables


Contingency table

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


Gender and l or r handed

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)


Gender and l or r handed1

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)


Gender and l or r handed2

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)


Probability p a part whole

ProbabilityP(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 whole1

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)?


How to complete a contingency table

How to complete a contingency table


Use the subtotals and information given

Use the subtotals and information given


Use the subtotals and information given1

Use the subtotals and information given


Conditional probability p a b

Conditional ProbabilityP(A | B):

A and B are two events,

the conditional probability that A occurs given that B already has

“P(A | B)”


What is the probability that the car is a ferrari given that it is black

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


What is the probability that the car is black given that it is a bugetti veron

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


Probability and contingency tables

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).


Complimentary events a and a a a 1

Complimentary eventsA and A (A + A = 1)

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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

Example:Will the Frog Fall?

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  • 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

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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