We usually write P() for the probability P({}) of an event containing only one point in .

We usually write P(ω) for the probability P({ω}) of an event containing only one point in .

Example 1.23 (Equiprobable outcomes) If  = {ω1,ω2, . . . ,ωN } and P(ωi ) = P(ωj ) for all i and j , then P(ω) = 1/N for ω ∈ , and P(A) = |A|/N for A ⊆ .

Exercise 1.25 Show that if a coin is tossed n times, then there are exactly 
n k 
= n!
k! (n − k)!