Question

When two six-sided dice are rolled, there are 36 possible outcomes. Find the probability that the sum is not 5.

Answer 1

Answer:

$p(Not\ 5) = \frac{8}{9}$

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.

$P(E)=\frac{n(E)}{n(S)}$  ----------------(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.

$P(5)=\frac{4}{36}$

$p(5) = \frac{1}{9}$

Using formula.

$p(Not\ E) + p(E) = 1$

$p(Not\ 5) + p(5) = 1$

Now we substitute p(5) in above equation.

$p(Not\ 5) + \frac{1}{9} = 1$

$p(Not\ 5) = 1-\frac{1}{9}$

$p(Not\ 5) = \frac{9-1}{9}$

$p(Not\ 5) = \frac{8}{9}$

Therefore, the sum of two six-sided dice roll outcome is not equal to 5.

$p(Not\ 5) = \frac{8}{9}$