Probability and Statistics Flashcards
Sample space
All of the possible outcomes (not the number of them!)
Probability of event A
Number of ways event A can happen/total number of equally likely outcomes
How would this be solved:
How many three letter combinations can be made from the 26 letters?
26^3=18576
How would this be solved:
How many different ways can you arrange 3 books from a group of 10 best sellers in a
store window?
10x9x8=720
Options per slot
Permutation
Arrangement of objects in a certain order
P(n,r)
Number of permutations of n objects taken r at a time
nPr=?
n!/(n-r)!
n!
N-factorial
6!
6x5x4x3x2x1= 720
Permutation for n objects with a objects of one kind, b objects of another, c objects of another…
n!/a!b!c!
Combination
An arrangement of objects in which order does not matter
nCr
Number of combinations for n objects taken r at a time
nC1=?
n
nCn=?
1
How would this be solved:
A pizza company offers 3 meat toppings and 9 vegetable toppings. How many different pizzas could be ordered if you wanted 2 meats and 3 veggies?
3C2x9C3
Independent events
Events in which the occurrence or nonoccurrence of one has no effect on the likelihood of the other
Dependent events
Events in which the occurrence or nonoccurrence of one affects the likelihood of the other
How to find the probability of two independent events both occurring:
P(A and B)= P(A)xP(B)
Mutually exclusive events
Events that cannot occur at the same time
Inclusive events
Events that can occur at the same time
How to find the probability of one of multiple mutually exclusive events happening
P(A or B)=P(A)+P(B)
How to find the probability of one of multiple inclusive events occurring
P(A or B)=P(A)+P(B)-P(A and B)
Remember: P(A and B) is found with P(A)xP(B)
How would this be solved:
There are seven ice cream flavors to choose from. You choose five randomly. You cannot choose one twice. What is the probability that your sundae will include both chocolate and vanilla?
1x5C3/7C5
Possibilities with both x other flavors in sundae/total possibilities
How would this be solved:
There are seven ice cream flavors to choose from. You choose five randomly. You cannot choose one twice. What is the probability that your sundae will include neither chocolate or vanilla?
5C5/7C5
Possibilities without chocolate or vanilla/total possibilities
