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probability
- P(E) = m/n
- m= #desired outcomes
- n= total # of outcomes
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Independence
- if the occurrence of one event does not effect the probability of the other
- ie: probability of first having a boy, then having a second child a boy (1/2)
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Addition rule
- the "or" rule
- P(A or B) = P(A) + P(B)
- ie: probability of rolling a 5 or 6 on die (1/6 + 1/6) = 2/6 = 1/3
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Multiplication rule
- the "and" rule
- for independent events..the probability of BOTH events occurring
- ie: probability of A_bb from a AaBb x AaBb dihybrid cross
- P(A_) * P(bb) = 3/4 * 1/4 = 3/16
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Binomial expansion
- Used for calculating the probability of MULTIPLE outcomes occurring
- 1. Calculate the # of outcomes that satisfy the question
- 2. Probability of each permutation
- P(outcome) = (n!/a!*b!)p^a * q^b
- n = # of trials
- a = # of p results
- b = # of q results
- p = probability of a
- q = probability of b
- ie: if Aa x Aa have 4 kids, what is the prob of getting 3 A_ and 1 aa?
- P = (4!/3! * 1!) (3/4)^3 * (1/4)^1
- P = 27/64
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Binomial Expansion w/MULTIPLE terms
- P = (n!/a!b!c!d!)p^a * q^b * r^c * s^d
- a+b+c+d = n
- q+r+s+t = 1
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Outcomes
- formula for how many outcomes are possible (ie: how many combinations of 2 hats you can pick out of a set of 5)
- nCr = n!/(n-r)! * r!
- n = total number
- r = # of selections
- outcomes = 5! / (5-2) * 2! = 10
- ALTERNATE is Pascal's triangle:
- go to the 5th row, and count from left to right starting from 0, 1, 2 (end at 2 since you are picking 2 hats)
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At Least One
- probability of At least one occurrence
- ie: probability of eldest girl of 3 children having AT LEAST ONE brother
- P = P(1st brother) + P(2nd brother) - P(both being brothers)
- P = 1/2 + 1/2 - (1/2*1/2)
- P = 1 - 1/4 = 3/4= 75%
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Chi Squared test
- 1. add all X^2 values (each value is a n)
- X^2 = (O-E)^2/E
- 2. calculate degrees of freedom
- df = (n-1)
- 3. look at chart and see if is Greater than 0.05
- 4. If is greater than 0.05, then FAIL TO REJECT hypothesis (Ho)
- 5. If is .05 or less, then REJECT Ho and ACCEPT Ha (alternate hypothesis)
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