Question

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.

Answer 1

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 = $\frac{880}{892}$

Probability of tickets that win a free adoption = $\frac{11}{892}$

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

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)

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

= $\frac{4117}{892}$

= $4.61 ⇒ this much amount expect to earn.