Question

1. A single 6-sided die is rolled. What is the probability of each outcome? What is the probability of rolling an even number? What is the probability of rolling an odd number?

2. Two 6-sided dice are rolled. Write the number of possible of rolling dice that add up to (a) 4, (b) 6 and (c) 8.

Answer 1

1. A single 6-sided die is rolled

Sample space

S = {1,2,3,4,5,6}

Here we have a total of 6 possibilities

So the probability of each outcome = 1/6

Let A be the event of rolling an even number

A = {2,4,6}

n(A) = 3

So the probability of rolling an even number

= n(A) / n(S) = 3/6 = 1/2

Let B be the event of rolling an even number

B = {1,3,5}

n(B) = 3

So the probability of rolling an even number

= n(B) / n(S) = 3/6 = 1/2

2. Two 6-sided dice are rolled.

Sample space

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)}

n(S) = 36

a)number of possible of rolling dice that add up to 4

Let A be the event that number of possible of rolling dice that add up to 4

A = {(1,1) (1,2) (1,3)

(2,1) (2,2)

(3,1) }

n(A) = 6

(b) the number of possible of rolling dice that add up to 6

Let B be the event that number of possible of rolling dice that add up to 6

B = {(1,1) (1,2) (1,3) (1,4) (1,5)

(2,1) (2,2) (2,3) (2,4)

(3,1) (3,2) (3,3)

(4,1) (4,2)

(5,1) }

n(B) = 15

(c)

Let C be the event that number of possible of rolling dice that add up to 8

C = {(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)

(4,1) (4,2) (4,3) (4,4)

(5,1) (5,2) (5,3)

(6,1) (6,2) }

n(C) = 26

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