Question

A pair of dice is tossed. what is the probability of getting sum of 5 or 9?

A)7/9
B)5/9
C)1/9
D)2/9​

Answer 1

`Probability = (2)/(9)`

Explanation:

Given:

A pair of dice

Required

Determine the probability of a sum of 5 or 9

Let the sample space of the first die be S1 and the second, S2

`S_1 = {1,2,3,4,5,6}` --- 6 outcomes

`S_2 = {1,2,3,4,5,6}` --- 6 outcomes

Number of sample space, n is:

`n = 6 * 6`

`n = 36`

Next, we list out all possibilities of obtaining a sum of 5

`Sum\ of\ 5 = \{(1,4),(2,3),(3,2),(4,1)\}`

n(Sum5 )= 4

Next, we list out all possibilities of obtaining a sum of 9

`Sum\ of\ 9 = \{(3,6),(4,5),(5,4),(6,3)\}`

n(Sum9)= 4

The required probability is then calculated as:

`Probability = (n(Sum9))/(Total) + (n(Sum5))/(Total)`

`Probability = (4)/(36) + (4)/(36)`

Take LCM

`Probability = (4+4)/(36)`

`Probability = (8)/(36)`

Simplify

`Probability = (2)/(9)`