Question

A scratch-off lottery ticket costs 5 dollars. If the ticket wins, it can be redeemed for 100 dollars. If the ticket loses, the ticket is worthless. According to the lottery's website, 4% of all tickets are winners. The expected value of buying a ticket is -1 dollar.

Which of the following statements are true?

A) The expected value of a ticket purchase is negative.
B) The probability of winning a prize is 4%.
C) The lottery ticket is a good investment.
D) Buying a ticket guarantees a win.

Answer 1

The student's question pertains to the expected value of a lottery ticket. Two statements are correct: the expected value is negative and the chance of winning is 4%. The lottery ticket is not a good investment due to the negative expected value.

Step-by-step explanation:

The student is asking about the concept of expected value in the context of a lottery ticket scenario. Expected value is a fundamental concept in probability and statistics used to predict the long-term outcome or average of a random event when it is repeated many times.

According to the given information, the cost of a lottery ticket is $5, the prize for a winning ticket is $100, and the winning probability is 4%. To calculate the expected value (EV) of purchasing a ticket, we use the formula EV = (probability of winning) x (amount won per winning ticket) + (probability of losing) x (amount lost per losing ticket).

Thus, EV = (0.04 x $100) + (0.96 x -$5) = $4 - $4.80 = -$0.80. Therefore, the expected value of a ticket purchase is negative, specifically -$0.80, not -$1 as stated. Statement A is true, B is true, and D is false because a win is not guaranteed. Based on the negative expected value, Statement C, 'The lottery ticket is a good investment,' is false.