A raffle is being held to benefit the local animal shelter. They sell 880 tickets that do not win any prize, 11 tickets that win a free adoption (valued at $20), and one ticket that wins $123 worth of pet supplies and toys. If they are selling the tickets for $5 each, how much should the shelter expect to earn for each ticket sold?

Round to the nearest cent, as needed.

Respuesta :

Answer: $4.61 this much amount expect to earn

Step-by-step explanation:

Given that,

Total number of tickets that do not have prize = 880

Tickets that win a free adoption (valued at $20) = 11

Ticket that wins $123 worth of pet supplies and toys = 1

So, total ticket sold = 880 + 11 + 1

                                = 892

Probability of tickets that not getting any prize = [tex]\frac{880}{892}[/tex]

Probability of tickets that win a free adoption = [tex]\frac{11}{892}[/tex]

Probability of tickets that wins $123 worth of pet supplies and toys = [tex]\frac{1}{892}[/tex]

Ticket value for no prize = $5

Ticket value that win a free adoption = -$20 + $5 = -$15

Ticket value that wins $123 worth of pet supplies and toys = -$123 + $5 = -$118

Expected return for each ticket = Σ(probability)(value of ticket)

 =  [tex]\dfrac{880}{892} \times5 + \dfrac{11}{892} \times (-$15) +\dfrac{1}{892}\times(-118)[/tex]

= [tex]\frac{4117}{892}[/tex]

= $4.61 this much amount expect to earn.