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 gain of $0.55 a gain of $0.45 a loss 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 gain of $0.55 a gain of $0.45 a loss 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. There is one $25$ gift - certificate, one $15$ gift - certificate, and three $5$ gift - certificates. So the total value of prizes $V=25 + 15+3\times5=25 + 15 + 15=55$.

Step2: Calculate the probability of winning

There are 100 tickets sold. The probability of winning a prize with one ticket $P=\frac{1}{100}$ for each individual ticket.

Step3: Calculate the expected value of winning

The expected value of winning $E$ is the product of the probability of winning and the total value of prizes. So $E=\frac{55}{100}=0.55$.

Step4: Calculate the cost of the ticket

The cost of one ticket is $C = 1$.

Step5: Calculate the expected profit or loss

The expected profit or loss $L$ is the expected value of winning minus the cost of the ticket. So $L=0.55−1=- 0.45$.

Answer:

a loss of $0.45$