Question

A lottery has a grand prize of $380,000, three runner-up prizes of $76,000 each, seven third-place prizes of $9500 each, and twenty-four consolation prizes of $760 each. If 760,000 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 return on a $1 ticket. (Round your answer to two decimal places.)

Answer 1

Solution:

Total number of tickets sold = 760000

Probability = Number of favourable event/Total number of event

The probability of winning $380,000 is

P(winning $380000) = 1/760000

The probability of winning $76,000 is

P(winning $76000) = 3/760000

The probability of winning $9500 is

P(winning $9500) = 7/760000

The probability of winning $760 is

P(winning $760) = 24/760000

Total probability of winning = (1+3+7+24)/760000

= 35/760000

Now,

The probability of lossing $1 is

P(lossing $1 ) = 1-(35/760000) = 759965/760000

The expected net winnings on a $1 ticket :

^{= (1*380000)/760000 + (3*76000)/760000 + (7*9500)/760000 + (24*760)/760000 - 759965/760000}

^{= (380000+228000+66500+18240-759965)/760000}

^{= -67225/760000}

^{= 0.0884}

^{= -0.09}

Therefore the expected net winnings on a $1 ticket is -0.09