Answer:
A.) - 2.8
B.) 0.2
Explanation:
Ticket price = $3
Winning price = $100
Probability of the winning(Pwin) = (1/500)
Probability of the not winning (Ploss) = [ 1 - (1/500)] = 499/500
Net income if Raul wins (Nwin) = $100 - $3 = $97
Net loss if Raul loss (Nloss) = - $3
A.) Calculation of Expected value
(Pwin × Nwin) + (Ploss × Nloss)
((1/500) × 197) + ((499/500) × - 3)
0.194 - 2.994 = - 2.8
B.) Calculation of Fair Value ;
Cost of ticket + Expected value
3 - 2.8 = 0.2
Answer:
A) he would make a loss of $2.79 of his ticket purchase hence the expected value of the ticket will be $3 - $2.79 = $0.21
B) fair price of a ticket = $0.20
Explanation:
A) The expected value
The variables are : winner prize = +$100 and -$3 ( not refunded )
The probability of winning the prize = 1/500 and 499/500 for not winning
therefore the expected value E(x) would be
= 100 * 1/500 + ( -3 ) * 499/500
= $0.2 - $2.99
= -$2.79 he would make a loss of $2.79 of his ticket purchase hence the expected value of the ticket will be $3 - $2.79 = $0.21
B) the fair price of the ticket would be
lets assume the fair price to be "y"
The random variables are $100 and -y
the corresponding probabilities of winning and not wining are : 1/500 and 499/500
= (100 * 1/500) + (-y * 499/500) = 0
= 100/500 - 499 y/500 = 0
= 100 - 499 y = 0
therefore y = 100 /499 = $0.20 fair value of the ticket
