A rattle offers a first prize of 300 2 second prizes of 100

A rattle offers a first prize of $300. 2 second prizes of $100 and 3 third prizes of $50 One ticket costs $4.00 and 500 tickets are sold. Find the expected winnings for one ticket. $130 -$2.70 $1.25 $2.65

Solution

P(getting first prize) = Number of first prize/Total tickets = 1/500

P(getting second prize) = Number of second prize/Total tickets = 2/500 = 1/250

P(getting third prize) = Number of third prize/Total tickets = 3/500

P(getting nothing) = Number of tickets with no prizes/Total tickets = 494/500

E(X) = Probability of X * Value of X

=> Prob(coming first) * First place price + Prob(coming second) * second place price + Prob(coming third) * third place price

=> 1/500 * 300 + 2/500 * 100 + 3/500 * 50

=> 300/500 + 200/500 + 150/500

=> 650/500 = $1.30

Hence the expected value is equal to 1.30$