angelos pizza is having a ticket raffle to raise money for new soccer uniforms. a $1 ticket gives an even…

Explanation:

Step1: Calculate probabilities

There are 100 total tickets. The probability of winning each prize: For the $25 - gift - certificate, $P(25)=\frac{1}{100}$, for the $15 - gift - certificate, $P(15)=\frac{1}{100}$, for the three $5 - gift - certificates (total value $15), $P(15)=\frac{3}{100}$, and the probability of winning nothing $P(0)=\frac{100-(1 + 1+3)}{100}=\frac{95}{100}$.

Step2: Calculate expected value of winning

The value of winning for each case: For the $25 - gift - certificate, the net gain is $25 - 1=24$, for the $15 - gift - certificate, the net gain is $15 - 1 = 14$, for the three $5 - gift - certificates (net gain $15 - 1=14$), and for winning nothing, the net gain is $0 - 1=-1$. The expected value $E(X)$ is calculated as $E(X)=24\times\frac{1}{100}+14\times\frac{1}{100}+14\times\frac{3}{100}+(-1)\times\frac{95}{100}$.

Step3: Simplify the expected - value formula

$E(X)=\frac{24 + 14+42-95}{100}=\frac{80 - 95}{100}=- 0.15$. Since the cost of the ticket is $1$, the expected profit or loss is $-0.15-1=-0.55$.

Answer:

a loss of $0.55