Question

The chance of winning a lottery game is 1 in approximately 27 million. Suppose you buy a​ $1 lottery ticket in anticipation of winning the ​$7 million grand prize. Calculate your expected net winnings for this single ticket. Interpret the result.

Answer 1

expected net winnings -0.741

Step-by-step explanation:

given data

chance of winning = 1 in approximately 27 million

buy a​ lottery ticket = $1

win grand prize = $7

solution

we get here expected net winnings for this single ticket is

we consider here X be the winnings from the lotto game

so

Probability if win (X = 7000 000) =
`(1)/(27000000)`

and

Probability if not win (X = 0) =
`(26999999)/(27000000)`

so

Expected (X) = ∑x P(X=x)

Expected (X) =
`(7000000)/(27000000)` + 0

Expected (X) = 0.259

so that we have expected to win $0.25 but we pay $1 for ticket

as expected net winning is = 0.259 - 1 = -0.741

it is negative so so it is expected loss