Answer:
[tex]Probability = \frac{2}{9}[/tex]
Step-by-step 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
[tex]S_1 = {1,2,3,4,5,6}[/tex] --- 6 outcomes
[tex]S_2 = {1,2,3,4,5,6}[/tex] --- 6 outcomes
Number of sample space, n is:
[tex]n = 6 * 6[/tex]
[tex]n = 36[/tex]
Next, we list out all possibilities of obtaining a sum of 5
[tex]Sum\ of\ 5 = \{(1,4),(2,3),(3,2),(4,1)\}[/tex]
n(Sum5 )= 4
Next, we list out all possibilities of obtaining a sum of 9
[tex]Sum\ of\ 9 = \{(3,6),(4,5),(5,4),(6,3)\}[/tex]
n(Sum9)= 4
The required probability is then calculated as:
[tex]Probability = \frac{n(Sum9)}{Total} + \frac{n(Sum5)}{Total}[/tex]
[tex]Probability = \frac{4}{36} + \frac{4}{36}[/tex]
Take LCM
[tex]Probability = \frac{4+4}{36}[/tex]
[tex]Probability = \frac{8}{36}[/tex]
Simplify
[tex]Probability = \frac{2}{9}[/tex]
