What is the expected value when a $1 lottery ticket is bought in which the purchaser wins exactly $10 million if the ticket contains the six winning numbers chosen from the set {1, 2, 3,…, 50} and the purchaser wins nothing otherwise?

We expect to lose $0.37 per lottery ticket

Explanation:

six winning numbers from = { 1, 2, 3, ....., 50}

So, the probability of winning:

The probability of losing would be:

P(loss) = 1 - P(win)

According to the question,

When we win, then we gain $10 million and lose the cost of the lottery ticket.

So,

$10,000,000 - 1 = $9,999,999

When we lose, then we lose the cost of the lottery ticket = $1

The expected value is the sum of the product of each possibility x with its probability P(x):

E(x) = ∑ xP(x)

Thus, we expect to lose $0.37 per lottery ticket

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