Question

a probability experiment is conducted in which the sample space of the experiment is ( s={8,9,10,11,12,13,14,15,16,17,18,19} ). let event ( e={10,11,12,13,14,15,16,17} ). assume each outcome is equally likely. list the outcomes in ( e^{c} ). find ( pleft(e^{c}
ight) ). list the outcomes in ( e^{c} ). select the correct choice below and, if necessary, fill in the answer box to complete your choice. ( \bigcirc mathrm{a} ). ( e^{c}= ) (use a comma to separate answers as needed ) ( \bigcirc mathrm{b} ). ( e^{c}={} )

Explanation:

Step1: Find the complement of event \(E\)

The complement of an event \(E\), denoted as \(E^{c}\), consists of all outcomes in the sample space \(S\) that are not in \(E\).
Given \(S=\{8,9,10,11,12,13,14,15,16,17,18,19\}\) and \(E = \{10,11,12,13,14,15,16,17\}\)
\(E^{c}=\{8,9,18,19\}\)

Step2: Calculate the probability of \(E^{c}\)

The formula for probability is \(P(A)=\frac{n(A)}{n(S)}\), where \(n(A)\) is the number of elements in event \(A\) and \(n(S)\) is the number of elements in the sample space.
Here, \(n(E^{c}) = 4\) and \(n(S)=12\)
\(P(E^{c})=\frac{4}{12}=\frac{1}{3}\)

Answer:

A. \(E^{c}=\{8,9,18,19\}\)
\(P(E^{c})=\frac{1}{3}\)