Question

Assume that a fair die is rolled. The sample space is , 1, 2, 3, 4, 56, and all the outcomes are equally likely. Find P8. Express your answer in exact form.

Answer 1

Answer:

$P\left(8\right)=0$

Step-by-step explanation:

Assuming that a fair die is rolled.

• The sample space is 1, 2, 3, 4, 5, 6 and all the outcomes are equally likely.

Let  X  be the set of all possible outcomes. Let  A  be an outcome.

So, the probability that  A  occurs is:

                                                        $P\left(A\right)=\frac{|A|}{|X|}$

As the set of all possible outcomes of the roll of a single die is:

$X=\left\{1,2,3,4,5,6\right\}$

Observe that

$|X|=6$

Here  

$|A|=0$   because 8 is not in the set sample space. So, the outcome of occurring the number 8 is not possible from the all possible outcomes.

So, the probability must be zero.

In other words,

                        $P\left(A\right)=\frac{|A|}{|X|}$

                         $P\left(8\right)=\frac{0}{6}=0$

Therefore,

                   $P\left(8\right)=0$