Question

For the following exercises, assume two die are rolled.

What is the probability of rolling a pair?

Answer 1

Consider rolling of two dice.

 

The sample space for the given experiment is

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

 

So, total number of possible outcomes is n(S) = 36.

 

Assume that E represents the event of rolling a pair. Then,

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

 

So, number of outcomes in the event E is n(E) = 6.

 

Consider the formula for the probability of an event with equally likely outcomes,

P(E) = n(E)/n(S) ...... (1)

 

From formula (1), the probability of rolling a pair will be,

P(E) = n(E)/n(S)

       = 6/36

       = 1/6