SOLUTION: 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 ticke

Question 1135432: 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?
Answer by VFBundy(438) (Show Source): You can put this solution on YOUR website!
1% of the time, a ticket wins $10, minus $5 for the cost of the ticket, meaning a net of gain $5.

0.1% of the time, a ticket wins $100, minus $5 for the cost of the ticket, meaning a net gain of $95.

0.000002% of the time, a ticket wins $1000000, minus $5 for the cost of the ticket, meaning a net gain of $999995.

If you add all these together and subtract from 100%, this is the percentage of losing tickets:
100% - 1% - 0.1% - 0.000002% = 98.899998% of the tickets lose $5.

The expected value:

0.01 * 5 = 0.05
0.001 * 95 = 0.095
0.00000002 * 999995 = 0.0199999
0.98899998 * (-5) = -4.9449999

Add all these together:
0.05 + 0.095 + 0.0199999 - 4.9449999 = -4.78

The expected value of a lottery ticket is -$4.78.
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