Question

Considering the 36 possible pairs of numbers (faces) when a pair of fair dice is rolled.

1. Define two events that are mutually exclusive (also called “disjoin events”). Apply your definition to the sample space of the dice-rolling experiment and clearly state what the two typical mutually exclusive events are.

2. Define two events that are statistically independent. Apply your definition to the sample space of the dice-rolling experiment and clearly state what the two typical statistically independent events are.

Answer 1

1)

event 1 - getting 2 on both dice

event 2 - getting 3 on both dice

event 1 - (2,2)

event 2 - (3,3)

probability that both event 1 and event 2 occurs = 0

P(A and B) = 0

hence they are mutually exclusive

2)

event 1 - getting 1 or first dice

event 2 -getting 2 on second dice

event 1 = {(1,1),(1,2),(1,3),(1,4),(1,5),(1,6)}

event 2 = {(1,2),(2,2),(3,2),(4,2),(5,2),(6,2)}

event 1 and event 2 = {(1,2)}

P(A) = 1/6

P(B) = 1/6

P(A and B) = 1/36

since

P(A and B) = P(A)P(B)

A and B are independent