If you roll two dice,

Question

what is the probability of the sum being 6 or 12?

Answer 1

When rolling two dice,

• Let (a , b ) is denote a possible out come of rolling the two die, with a is the number on the top of the first die, and b is the number on the top of the second die.

Note that each of a  and b  can be any of the integers from 1 through 6.

Here is a listing of all the joint possibilities for (a , b )

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

Note that we have listed all the ways a first die and second die sum being 6 when we look at their top faces.

In general, when the two dice are fair and independent, the probability of any event is the number of elements in the event divided by 36.

P(E₁) = 6/36 = 1/6.

→ P(E₁) = 1/6.

• Note that each of a  and b  can be any of the integers from 1 through 6.

Here is a listing of all the joint possibilities for (a , b )

Event E = {(6 , 6)}

Note that we have listed all the ways a first die and second die sum being 12 when we look at their top faces.

In general, when the two dice are fair and independent, the probability of any event is the number of elements in the event divided by 36.

P(E₂) = 1/36.

→ P(E₂) = 1/36.

• Probability of the sum being 6 (or) 12 means that,

P(6 or 12) = P(E₁ or E₂) = P(E₁) + P(E₂)

= 1/6 + 1/36

= 7/36.

Therefore, the probability of the sum being 6 or 12 is 7/36.