Question

A lottery has a grand prize of $100,000, four runner-up prizes of $20,000 each, nine third-place prizes of $2000 each, and twenty-one consolation prizes of $200 each. If 300,000 tickets are sold for $1 each and the probability of any one ticket winning is the same as that of any other ticket winning, find the expected net winnings on a $1 $ 157 ticket. (Round your answer to two decimal places.)

Answer 1

TOPIC:Expected value of a random variable.

=) Let, x= Net winnings of the lottery based on a single & I ticket. (in $. Consider the following table as Outcomes Price of Net winning (²) the ticket ($) +/= amount won the nicker Ticket Price Probability P(x) Winning the grand prize 100,000 -1 = 99,999 300,000 Winning the а Younnet - up prize 1 20,000-1 = 19,999 4 300,000 9 Winning a thind- place prize 2000 -1 = 1999 300,000 winning A consolation prize 200- = 199 300,000 Winning nothing 0-1 = -1 299, 965 300,000 I : There is only one grand prize, dour punner-up proizes, nine third-place prizes, 21 consolation prizes and the rest (300,000 -1-4-9-21) 2 299, 965 tickets, where the person wins nothing. So, P (of winning the grand prize) = 100 P(" " " second-place (runner 300,000 prize 300,000

Proceeding in this way, p (of winning nothing) = 205, 200 winning nothing 299, 965 300,000 i we need, a) Expected net gain (winnings) on a $ 1 tichet. = E(X). - EXP(). = 99, 999 x 1 300,000 + 19, 999 x - - 300,000 t 1999 X 300,000 + 199 x 300,000 + ) x 299,965 300,ooo - - 0.326, ~ $ 0.33 (Rounded to two decimals ie. The net loss person has an expected of $ 0.33. (Ans).

Answer : $ - 0. 33