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 $0.45 a gain of $0.55 a loss 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 $0.45 a gain of $0.55 a loss of $0.55 a gain of $0.45

Answer

Explanation:

Step1: Calculate total value of prizes

The total value of prizes is the sum of the values of all gift - certificates. One $25$ gift - certificate, one $15$ gift - certificate, and three $5$ gift - certificates. So, $25 + 15+3\times5=25 + 15 + 15=55$.

Step2: Calculate probability of winning

There are 100 tickets sold. The probability of winning any prize with one ticket is $\frac{1}{100}$ for each individual winning outcome.

Step3: Calculate expected value of winning

The expected value of winning $E(X)$ is calculated as follows. The probability of winning the $25$ - dollar certificate is $\frac{1}{100}$, the probability of winning the $15$ - dollar certificate is $\frac{1}{100}$, and the probability of winning a $5$ - dollar certificate is $\frac{3}{100}$. So, $E(X)=25\times\frac{1}{100}+15\times\frac{1}{100}+5\times\frac{3}{100}=\frac{25 + 15+15}{100}=\frac{55}{100}=0.55$.

Step4: Calculate expected profit or loss

The cost of a ticket is $1$. The expected profit $P$ is the expected value of winning minus the cost of the ticket. So, $P = 0.55-1=- 0.45$.

Answer:

a loss of $0.45$