How do you find the following PROB 22 22 A sample space S is

How do you find the following?

PROB 2.2:

2.2 A sample space S is given to be {a1,a2,a3,a4,a5,a6}. The following events are defined on this sample space: A1= 2.5 Consider the sample space in Prob 2.2 in which all the outcomes are assumed equally likely. Find the following probabilities.

Solution

a. We find A1.A2 which is logically the intersection of A1 and A2:

A1.A2 = {a₂}

P(A1.A2) = P(a₂) = 1/6

b. We find A1+A2 which is logically the union of A1 and A2:

A1+A2 = {a_1,a₂,a_3,a_4,a₆}

P(A1+A2) = P(a₁) + P(a₂) + P(a₃) + P(a₄) + P(a₆) = 5/6

c. We find (A1+A3^c ).A2 = (a₁,a₂,a₄,a₆).A2 = (a₂, a₆)

P[(A1+A3^c ).A2] = P(a₂) + P(a₆) = 2/6 = 1/3