Ch. 2 Equally likely outcomes

Question 1

Consider a scenario with m equally likely outcomes, {ω1 , … , ωm} = Ω
In the equally likely outcomes model, P(A), A c Ω, is

Answer 1

P(A) := mA/m

Where mA is the number of outcomes in the event A

Question 2

|A| =

Answer 2

The number of outcomes in the event A

Question 3

Suppose we must make k choices in succession where there are:
m1 possibilities for the first choice
m2 possibilities for the second choice
….
mk possibilities for the kth choice
Total no of distinct possible selections is:

Answer 3

m1 x m2 x m3 x …. x mk

Question 4

Suppose we have m distinct objects and we select r less than or equal to m of them without replacement, no of ordered lists is

Answer 4

m! / (m-r)!

Question 5

Suppose we have m distinct objects and we select r less than or equal to m of them without replacement, no of distinct subsets of size r is:

Answer 5

m! / r!(m-r)!

m choose r