Probability Flashcards
Fundamental counting principle
Total possible answers * amount chosen
Find the order of something
Amount of numbers factorial
Permutation
No option can be used more than one
Order matters
nPr
Combination
Options can be used multiple times
Order does not matter
nCr
find sample space
tree diagram
P(AlB)
P(AnB)/P(B)
P(BlA)
P(AnB)/P(A)
P(AuB)
P(A) + P(B) - P(AnB)
P(AlAuB)
P(A)/P(AuB)
What is P(AB) the same as
P(AnB)
3rd way to tell if something is independent or dependent
P(AnB) = P(A) * P(B)
How to tell if groups are independent
Find the probability for group A
Find group B
Find A n B by dividing the number in the first group by the total
Multiply A and B together
If it equals A n B, it is independent
Binomial Expansion
Write down how many x’s you have and the numbers in front of them
Put the leading coefficients of x and y in front of the numbers.
Only raise the number to a power if it is directly next to it
Combine like terms
Finding a term in a binomial **
subtract the power that the binomial is raised to by the power that you are trying to find
put the binomial’s number over top of the subtracted number
raise the leading coefficient of x to the desired power
raise the lc of y to the subtracted power
multiply nCr by the two numbers
must put the x+y in the answer
Find the numbers/letters w/ no repeats
letters; multiply 26 by itself getting smaller by 1 each time
number
Numbers: multiply 10 by itself getting smaller by 1 each time
multiply them
Find the numbers and letters with repeats
Letters: 26^however many numbers there are
Numbers 10^amount of numbers
Multiply them
Creating groups without regard to order
Make combinations with the total amount C the amount you’re trying to find
Finding the probability of specific things with replacement
create a fraction with number of possible objects/total objects * the same fractions for number of trials
Find the probability of specific things without replacement
create a fraction with number of possible objects/total objects * subtract 1 for every trial
Binomial probability formula
(n/r) p^r * q^n-r
N=# of trials
r= # of successes
P= probability of sucesses
q= probability of failure
More than once formula
1-P(X=0) - P(x=1)
less than/equal to once
1-P(X=0)
