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 gain of $0.45 a loss of $0.55

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 gain of $0.45 a loss of $0.55

Answer

Explanation:

Step1: Calculate probability of winning

There are 5 prizes in total (1 $25, 1 $15, 3 $5) and 100 tickets sold. The probability of winning a prize with 1 ticket is $\frac{5}{100}=0.05$, and the probability of not - winning is $1 - 0.05 = 0.95$.

Step2: Calculate expected value of winning

The value of winning:

  • For the $25 gift - certificate: $25\times\frac{1}{100}=0.25$
  • For the $15 gift - certificate: $15\times\frac{1}{100}=0.15$
  • For the $5 gift - certificate: $5\times\frac{3}{100}=0.15$ The sum of the expected values of winning is $0.25 + 0.15+0.15=0.55$.

Step3: Calculate expected profit or loss

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

Answer:

a loss of $0.45