Answer to Question #298426 in Statistics and Probability for Lester San Juan

Question

A lottery that pays off P300 000 000 is made available for 10 000 000 tickets. Each ticket costs P50. Suppose the variable Z gives the net winnings from playing the lottery. What is the expected gain for joining the lottery with only one ticket?

Answer 1

Solution:

The expected gain of a ticket is:

= (1 / 10000000) $\times$ [(300000000 - 50) + {(10000000 - 1) $\times$ (-50)}]

= (1 / 10000000) $\times$ (299999950 - 499999950)

= (1 / 10000000) $\times$ (-200000000)

= -20

A person who continues to play this lottery for a very long time will probably win some money occasionally but on average will lose P20 per ticket.