Final answer:
The expected monetary value of a single lottery ticket with a 1 in 15,000,000 chance of winning a $45,000,000 prize is just over $2, after accounting for the price of the ticket. This is calculated by weighing the probability of winning against the potential prize and the cost of the ticket.
Step-by-step explanation:
To calculate the expected monetary value of a single ticket in the given scenario, we need to consider the probability of winning and the potential prize amount. The chance of winning is given as 1 in 15,000,000. Hence, the probability of winning is 1/15,000,000 and the probability of losing is (15,000,000 - 1)/15,000,000.
Using these probabilities, the expected value (EV) of a ticket can be calculated as:
EV = (Probability of Winning * Prize) - (Probability of Losing * Cost of Ticket)
Plugging in the values given:
EV = (1/15,000,000 * $45,000,000) - ((15,000,000 - 1)/15,000,000 * $1)
After calculation, the EV turns out to be:
EV = $3 - $0.999933333...
This results in the EV being slightly over $2.
This value assumes that if multiple people win, the prize would still be split evenly and not affect the individual expected value of a ticket. Given that the ticket costs $1, if the EV we calculated is more than $1, it signifies a lucrative bet from a strictly mathematical standpoint.