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

Answer

Explanation:

Step1: Calculate total prize money

There is one $25$ - dollar, one $15$ - dollar and three $5$ - dollar gift - certificates. So the total prize money is $25 + 15+3\times5=25 + 15 + 15=55$ dollars.

Step2: Calculate probability of winning

There are 100 tickets sold. The probability of winning for each ticket, $p=\frac{1}{100}$.

Step3: Calculate expected value of winning

The expected value of winning, $E(X)$ is the sum of the products of each prize amount and its probability. The probability of winning each of the 5 prizes (1 of $25$, 1 of $15$, 3 of $5$) is $\frac{1}{100}$. So $E(X)=\frac{25 + 15+3\times5}{100}=\frac{55}{100}=0.55$ dollars.

Step4: Calculate expected profit or loss

The cost of a ticket is $1$ dollar. The expected profit or loss $=E(X)-1$. Substituting the value of $E(X)$, we get $0.55−1=- 0.45$ dollars.

Answer:

a loss of $0.45$