Answer:
[tex]p(Not\ 5) = \frac{8}{9}[/tex]
Step-by-step explanation:
Given:
Txo six-sided dice are rolled.
Total number of outcomes n(S) = 36
We need to find the probability that the sum is not equal to 5 p(Not 5).
Solution:
Using probability formula.
[tex]P(E)=\frac{n(E)}{n(S)}[/tex] ----------------(1)
Where:
n(E) is the number of outcomes favourable to E.
n(S) is the total number of equally likely outcomes.
The sum of two six-sided dice roll outcome is equal to 5 as.
Outcome as 5: {(1,4), (2,3), (3,2), (4,1)}
So, the total favourable events n(E) = 4
Now, we substitute n(E) and n(s) in equation 1.
[tex]P(5)=\frac{4}{36}[/tex]
[tex]p(5) = \frac{1}{9}[/tex]
Using formula.
[tex]p(Not\ E) + p(E) = 1[/tex]
[tex]p(Not\ 5) + p(5) = 1[/tex]
Now we substitute p(5) in above equation.
[tex]p(Not\ 5) + \frac{1}{9} = 1[/tex]
[tex]p(Not\ 5) = 1-\frac{1}{9}[/tex]
[tex]p(Not\ 5) = \frac{9-1}{9}[/tex]
[tex]p(Not\ 5) = \frac{8}{9}[/tex]
Therefore, the sum of two six-sided dice roll outcome is not equal to 5.
[tex]p(Not\ 5) = \frac{8}{9}[/tex]
