An online gambling site offers a first prize of $50000 and two second prizes of $20000 each for registered users when they place a bet. A random bet will be selected over a 24hour period. Two million bets are received in the contest. Find the expected winnings if you can place one registered bet of $1 in the given period.

−0.955

Explanation:

Given the following :

Worth of placing a registered bet = $1

1st price = $50,000

2nd price = $20,000

Total bets received = 2,000,000

Net winning :

Winning - worth of placing a registered bet

Ist price = $50,000 - $1 = $49,999

2nd price = $20,000 - $1 = $19,999

Amount lost = - $1

number of losers = 2,000,000 - 3 = 1,999,997

Probability :

Probability = (required outcome / Total possible outcomes)

Number of 1st price winners = 1

Number of second price winners = 2

P(1st price) = 1 / 2,000,000

P(2nd price) = 2/ 2,000,000 = 1/ 1,000,000

Therefore ;

Net winning (x) - - 49,999 - 19,999 - - - (-1)

P(winning) p(x) - - 1/2mill - - 1/1mill-- 1999997/2mill

Expected winnings = sum of [(x) * p(x)]

= ($49,999 * 0.0000005) + (19,999 * 0.000001) +(-1 * 0.9999985)

= 0.0249995 + 0.019999 − 0.9999985

= 0.0449985 - 0.9999985

= - 0.955