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elixir [45]
3 years ago
14

What is the expected value when a $1 lottery ticket is bought in which the purchaser wins exactly $10 million if the ticket cont

ains the six winning numbers chosen from the set {1, 2, 3,…, 50} and the purchaser wins nothing otherwise?
Business
1 answer:
Nadusha1986 [10]3 years ago
7 0

We expect to lose $0.37 per lottery ticket

<u>Explanation:</u>

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

So, the probability of winning:

P(win) = \frac{ no of favorable outcomes}{no of possible outcomes}

P(win) = \frac{1}{^5^0C_6} \\\\P (win) = \frac{6! X (50 - 6)!}{50!} \\\\P(win) = \frac{6! X 44!}{50!} \\\\P(win) = \frac{1}{15,890,700}

The probability of losing would be:

P(loss) = 1 - P(win)

P(loss) = 1 - \frac{1}{15,890,700} \\\\P(loss) = \frac{15,890,699}{15,890,700}

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)

= 9,999,999 X \frac{1}{15,890,700}  + ( -1 ) X \frac{15,890,699}{15,890,700} \\\\=- \frac{5,890,700}{15,890,700} \\\\= - \frac{58,907}{158,907} \\\\= - 0.37

Thus, we expect to lose $0.37 per lottery ticket

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