Answer
The expected value of a single ticket in the raffle = -1.36
Explanation
The expected of a single ticket in the raffle can be calculated using:
[tex]\begin{gathered} E(x)=\sum ^{}_{}x\mathrm{}p(x) \\ \text{Where x is the random variable and } \\ \text{P(x) is the probability of the random variable x} \end{gathered}[/tex]Since 7000 tickets are sold for $2 each, total amount of tickets sold would be = 7000 x 2 = $14,000
The probability of winning =
[tex]\frac{1}{14000}[/tex]The probability of losing =
[tex]1-\frac{1}{14000}=\frac{13999}{14000}[/tex]The gain or loss of winning =
[tex]9000-2=8998[/tex]The gain or loss of losing = -2
Therefore, the expected value E(x) of a single ticket in the raffle =
[tex]\begin{gathered} E(x)=8998(\frac{1}{14000})+(-2)\frac{13999}{14000} \\ E(x)=\frac{8998}{140000}-\frac{27998}{14000} \\ E(x)=-\frac{19000}{14000} \\ E(x)=-1.36 \end{gathered}[/tex]
