Question

A lottery is played with 40 numbers in the universe. A lottery ticket contains 6 distinct numbers. There are only two possibilities. You won 10 million dollars if your ticket exactly matches the 6 winning numbers. Otherwise you lose. There are no other prizes. A ticket costs $1. What is the expected value of this $1 ticket

Answer 1

The right answer is "1.6053".

Explanation:

According to the question,

The expected value will be:

=
`-Cost \ of \ ticket+Probability \ of \ winning* Winning \ amount`

As we know,

The probability of winning the lottery will be:

=
`(1)/(No. \ of \ ways \ of \ choose \ six \ from \ 40)`

So that, the expected value is:

=
`-1+\frac{10^7}{\binom{40}6}}`

=
`-1+(10^7)/(3838380)`

=
`1.6053`