SOLUTION: Robert bought a $2 lottery ticket such that 1 in 100 would win $9, 1 in 1000 would win $80, and 1 in 50 million would win 1 million. What is the expected value of a lottery ticket

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Question 1197108: Robert bought a $2 lottery ticket such that 1 in 100 would win $9, 1 in 1000 would win $80, 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?

Select an answer

By how much?
Answer by math_tutor2020(3817) (Show Source):
You can put this solution on YOUR website!

1 in 100 = 1/100 = 0.01
1 in 1000 = 1/1000 = 0.001
1 in 50 million = 1/(50 million) = 1/(50*10^6) = 0.00000002

Those probability values add to:
0.01+0.001+0.00000002 = 0.01100002
Subtract that from 1
1-0.01100002 = 0.98899998
This represents the probability of winning $0

X = net winnings = (amount won) - ($2 cost)
P(X) = probability of getting those net winnings

X P(X) X*P(X)
7 0.01 0.07
78 0.001 0.078
999998 0.00000002 0.01999996
-2 0.98899998 -1.97799996

Add up the values in the X*P(X) column
0.07 + 0.078 + 0.01999996 + (-1.97799996) = -1.81

The expected earnings for each lottery ticket, on average, is -1.81 dollars.
This means Robert expects to lose on average about $1.81 per ticket.

It doesn't matter how many tickets he buys. He won't earn a profit since the profit per ticket is negative.