Question

Consider a fair six-sided die. Suppose the event A is defined to be rolling an even number, and the event B is defined to be rolling a number less than 5.

a) Find P(A).

b) Find P(B^C)

c) Find P(A or B)

d) Find P(A and B)

e) Are the events A and B mutually exclusive/disjoint? Explain.

Answer 1

a)

There are three even numbers in a fair six-sided die.

P(A) = 3/6 = 1/2

b)

There are four numbers less than 5 in a fair six-sided die.

P(B) = 4/6 = 2/3

P(B^C) = 1 - P(B) = 1 - 2/3 = 1/3

c)

P(A or B) = Number of even number or less than 5 / Total numbers = 5/6

d)

P(A and B) = Number of even number and less than 5 / Total numbers = 2/6 = 1/3

e)

Since,  P(A and B) 0 , the events A and B are not mutually exclusive/disjoint.