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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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)
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)
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)
A = male wearing green
P(A) = 2/15
B = wearing red
P(B) given they are women
4/10
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)?
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 rain is 4/5).


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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


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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