Question

Robert bought a $5 lottery ticket such that 1 in 100 would win $10, 1 in 1000 would win $100, and 1 in 50 million would win 1 million. What is the expected value of a lottery ticket in dollars?

Does Robert expect to earn a profit if he buys 100 tickets?


By how much?

Answer 1

Loss of $4.78

Loss of $478

Explanation:

Expected value = Sum of (winning amount x winning probability) - cost of lottery ticket

Expected value = ( $10 x 1/100 + $100 x 1/1000 + $1 million x 1/$50 million ) - $5

Expected value= $0.22 - $5

Expected value= - $4.78

The Negative value of expected value indicates loss)

Amount expected to lose if 100 tickets are bought = 100 x $4.78 = $478