# Make a table in which you list all possible outcomes of rolling two dice. call the dice a and b.

What is the probability of rolling a 7.00? You can give the probabilities as fractions, such as 3/36.

What is the probability of any double?

What is the probability of rolling a 7.00 or an 8? You can give the probabilities as fractions, such as 3/36.

**Solution:**

The list of all outcomes of rolling two dices is nothing but sample space, which has following outcomes:

**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)}**

Here the total number of outcomes is 36.

Therefore,

n(S) = 36

**A: Rolling a 7.00 (Sum of the numbers on both the dice = 7.00) = {(1,6)(2,5)(3,4)(4,3)(5,2)(6,1)}**

Therefore,

n(A) = 6

P(A) = n(A)/n(S)

= 6/36 = 1/6

**B: Rolling of doublets = {(1,1)(2,2)(3,3)(4,4)(5,5)(6,6)}**

Therefore,

n(B) = 6

P(B) = n(B)/n(S)

= 6/36 = 1/6

**C: Rolling 7 or 8 (Sum of the numbers is 7 or 8) = {(1,6)(2,5)(3,4)(4,3)(5,2)(6,1)(2,6)(3,5)(4,4)(5,3)(6,2)}**

Therefore,

n(C) = 11

P(C) = n(C)/n(S)

= 11/36

## Make a table in which you list all possible outcomes of rolling two dice. call the dice a and b.

What is the probability of rolling a 7.00? You can give the probabilities as fractions, such as 3/36.

What is the probability of any double?

What is the probability of rolling a 7.00 or an 8? You can give the probabilities as fractions, such as 3/36.

**Summary:**

The possible outcomes of rolling two dice (i) probability of rolling a 7.00 = 1/6, (ii) probability of any double = 1/6 , (iii) probability of rolling a 7.00 or an 8 = 11/36.