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

angelos pizza is having a ticket raffle to raise money for new soccer uniforms. a $1 ticket gives an even chance to win one $25 gift certificate, one $15 gift certificate, or three $5 gift certificates. what is the expected profit or loss for purchasing 1 ticket if 100 total tickets are sold? a loss of $0.55 a loss of $0.45 a gain of $0.55 a gain of $0.45

angelos pizza is having a ticket raffle to raise money for new soccer uniforms. a $1 ticket gives an even chance to win one $25 gift certificate, one $15 gift certificate, or three $5 gift certificates. what is the expected profit or loss for purchasing 1 ticket if 100 total tickets are sold? a loss of $0.55 a loss of $0.45 a gain of $0.55 a gain of $0.45

Answer

Explanation:

Step1: Calculate total value of prizes

The total value of prizes is $25 + 15+3\times5=25 + 15 + 15=55$.

Step2: Calculate probability of winning

The probability of winning with 1 ticket out of 100 is $p=\frac{1}{100}$.

Step3: Calculate expected value of winning

The expected - value of winning $E(X)$ is the sum of the products of each outcome and its probability. The value of winning is the value of the prize minus the cost of the ticket. The probability of winning the $25 - dollar$ prize is $\frac{1}{100}$, the probability of winning the $15 - dollar$ prize is $\frac{1}{100}$, and the probability of winning a $5 - dollar$ prize is $\frac{3}{100}$, and the probability of winning nothing is $\frac{100-(1 + 1+3)}{100}=\frac{95}{100}$. $E(X)=(25 - 1)\times\frac{1}{100}+(15 - 1)\times\frac{1}{100}+(5 - 1)\times\frac{3}{100}+(0 - 1)\times\frac{95}{100}$ $=\frac{24}{100}+\frac{14}{100}+\frac{12}{100}-\frac{95}{100}$ $=\frac{24 + 14+12-95}{100}=\frac{50 - 95}{100}=-\frac{45}{100}=- 0.45$.

Answer:

a loss of $0.45$