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.