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

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Answer:

The right answer is "1.6053".

Step-by-step explanation:

According to the question,

The expected value will be:

= [tex]-Cost \ of \ ticket+Probability \ of \ winning\times Winning \ amount[/tex]

As we know,

The probability of winning the lottery will be:

= [tex]\frac{1}{No. \ of \ ways \ of \ choose \ six \ from \ 40}[/tex]

So that, the expected value is:

= [tex]-1+\frac{10^7}{\binom{40}6}}[/tex]

= [tex]-1+\frac{10^7}{3838380}[/tex]

= [tex]1.6053[/tex]