Combinatorics and Probability Flashcards
What is the Equation for Probability ?
P = x/n
x = Fav outcomes
n = All outcomes
How are the probability of an event and the probability of a non-event related ?
I = P(E) + P(E’)
For Single Events
P(A or B) = ?
P(A) + P(B)
Define for a set :
- Intersection
- Union
- Disjoint
Intersection –> Set of elements in common –> N
Union –> Elements in either set or both sets –> U
Disjoint –> No common elements –> Ø
How do you find the Number of Subsets of a Set ?
number of Subsets = 2^n
n = number of elements or entities
n^Cr = ?
n^Ci = ?
n^Cr = n.C(n-r)
n^Ci = n
How do you find the # of non empty subsets ?
2^(n) - 1
n = # elements or entities
In a set {a,b,c,d,e,f}
How do you find the probability of choosing b+d or a+c ?
(Ci^2)/(C2^6)
Top : –> Chance of Choosing either b+d or a+c
Bottom –> Chance of choo
For multiple events where you don’t know if events are independent - what do you do ?
Understand the event produced for A and B together to find favourable outcomes
With Permutation what is the impact when repetition is allowed ?
- # entities remains the same
O! =
1
Whats is the permutation formula ?
And when can it be used ?
Pr^n = n! / (n-r)!
Repetition is not allowed
For Arrangements with independent events
Treat each event as an individual space
When elements need to be together - arrangement of thos elements in the space = ?
(# elements) !
What is the difference between selection and arrangement ?
Arrangement = Order matters
Selection = Order irrelevant
