Question

A probability experiment is conducted in which the sample space of the experiment is S = (2,3,4,5,6,7,8,9,10,11,12). Let event A = {5,6,7,8,9). Assume that each outcome is equally likely List the outcomes

Answer 1

Case: Probability (Sample space)

Given:

Sample space, S = (2,3,4,5,6,7,8,9,10,11,12)

event A = {5,6,7,8,9)

Required: Get the list of elements for A complement and the probability of obtaining A complement.

Method:

A complement simply represents items found in the Sample space, S but not in event A.

It includes:

`A^c=\text{ (2,3,4,10,11,12)}`

The probability to obtain event A complement will be:

`\begin{gathered} Pr(A)+Pr(A^c)\text{ = 1} \\ \text{When you add two opposite events, it gives 1} \\ Pr(A^c)=\frac{numberofeventforA^c}{\\u mber\text{ of events for sample space}} \\ Pr(A^c)=\text{ }(6)/(11) \end{gathered}`

Final answer:

`\begin{gathered} A^c=\text{ (2,3,4,10,11,12) AND} \\ Pr(A^c)=\text{ }(6)/(11) \end{gathered}`