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. a. ( e^{c}={8,9,18,19} ) (use a comma to separate answers as needed.) b. ( e^{c}=() ) ( pleft(e^{c}
ight)=square ) (type an integer or a decimal rounded to three decimal places as needed.)

Explanation:

Step1: Calculate the number of elements in \(S\) and \(E^c\)

The sample space \(S=\{8,9,10,11,12,13,14,15,16,17,18,19\}\), so \(n(S) = 12\).
The complement event \(E^c=\{8,9,18,19\}\), so \(n(E^c)=4\).

Step2: Use the probability formula \(P(A)=\frac{n(A)}{n(S)}\)

For \(A = E^c\), we have \(P(E^c)=\frac{n(E^c)}{n(S)}\).
Substitute \(n(E^c) = 4\) and \(n(S)=12\) into the formula: \(P(E^c)=\frac{4}{12}=\frac{1}{3}\approx0.333\)

Answer:

\(P(E^c)\approx0.333\)