Question

You buy a lottery ticket to a lottery that costs $10 per ticket. There are only 100 tickets available to be sold in this lottery. In this lottery there are one $450 prize, two $120 prizes, and four $30 prizes. Find your expected gain or loss. (Round your answer to two decimal places.)

Answer 1

Answer:

Loss of $1.20

Step-by-step explanation:

The possible outcomes for this lottery and their probabilities are:

- a 1 in 100 chance of winning $450

- a 2 in 100 chance of winning $120

- a 4 in 100 chance of winning $30

- a 93 in 100 chance of losing $10

Therefore, the expected value of this lottery when buying one ticket is:

$E(X) = \frac{1}{100}*\ 450+ \frac{2}{100}*\ 120+ \frac{4}{100}*\ 30-\frac{93}{100}*\ 10 \\E(X) = -\ 1.2$

Therefore, you are expected to lose $1.2 per ticket.