Question

The chance of winning a lottery game is 1 in approximately 26 million. Suppose you buy a​ $1 lottery ticket in anticipation of winning the ​$4 million grand prize. Calculate your expected net winnings for this single ticket. Interpret the result.

Find μ=E(x).

μ=____________________​(Round to the nearest hundredth as needed. Do not include the​ $ symbol in your​answer.)

Answer 1

The chance of winning a lottery game is 1 in approximately 26 million

Probability ( Winning ) = P(w) = 1 / 26*10⁶

Prize = X = 4 * 10⁶

Expected prize = E ( X )

= 4 * 10⁶ ( 1 / 26*10⁶ )

= 0.15 $

Since you have paid $1 for the ticket, the net winnings is $0.15 - $1.00 = -$0.85

the net winnings is -$0.85

What this means is that, on average, you will lose 85 cents for every ticket that you will buy. we can interpret that the fair price for a lottery ticket is about 15 cents, and the lottery commission is getting over 85 cents on every ticket sold, even after the prizes are paid out.