Question

a probability experiment is conducted in which the sample space of the experiment is s = {1,2,3,4,5,6,7,8,9,10,11,12}. let event e = {2,3,4,5,6}. assume each outcome is equally likely. list the outcomes in e^c. find p(e^c). 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 = (use a comma to separate answers as needed.) b. e^c = {}

Explanation:

Step1: Define complement of event

The complement of event $E$, denoted as $E^c$, contains all outcomes in the sample - space $S$ that are not in $E$.
Given $S=\{1,2,3,4,5,6,7,8,9,10,11,12\}$ and $E = \{2,3,4,5,6\}$, we find $E^c$ by removing the elements of $E$ from $S$.

Step2: List the elements of $E^c$

$E^c=\{1,7,8,9,10,11,12\}$

Step3: Calculate the probability of $E^c$

The probability of an event $A$ in a sample - space with equally likely outcomes is given by $P(A)=\frac{n(A)}{n(S)}$, where $n(A)$ is the number of elements in event $A$ and $n(S)$ is the number of elements in the sample - space.
Here, $n(E^c) = 7$ and $n(S)=12$. So, $P(E^c)=\frac{7}{12}$

Answer:

$E^c=\{1,7,8,9,10,11,12\}$, $P(E^c)=\frac{7}{12}$