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

Answer

Explanation:

Step1: Calculate the total amount of money from selling tickets

The price of one ticket is $1$, and 100 tickets are sold. So the total money from selling tickets is $1\times100 = 100$ dollars.

Step2: Calculate the total amount of gift - certificates

There is one $25$ gift certificate, one $15$ gift certificate, and three $5$ gift certificates. The total value of gift - certificates is $25+15 + 3\times5=25 + 15+15=55$ dollars.

Step3: Calculate the expected value of one ticket

The probability of winning for one ticket: The total number of winning tickets is $1 + 1+3=5$ (since there are 5 prizes in total). The probability of winning $P(\text{win})=\frac{5}{100}=0.05$, and the probability of losing $P(\text{lose}) = 1 - 0.05=0.95$. The expected value $E(X)$ of the ticket (in terms of the amount won) is: [ \begin{align*} E(X)&=(25\times\frac{1}{100})+(15\times\frac{1}{100})+(5\times\frac{3}{100})+(0\times\frac{95}{100})\ &=\frac{25 + 15+15+0}{100}\ &=\frac{55}{100}=0.55 \end{align*} ] Since the cost of the ticket is $1$, the expected profit or loss is $E = 0.55-1=- 0.45$

Answer:

a loss of $$0.45$