A ticket in a typical lottery like Lotto 6/49 is usually $2. The
probability of winning Lotto 6/49 is 1 in 13,983,816. The payoffs
(jackpots) are usually in excess of $1 million. Suppose that you buy
one ticket for $2 and the jackpot is $1 million. What is your expected
value of gain or loss? Explain your expected value. Note: for this
question, create the mass function, then calculate the expected
value.
Lottery game is a mistery yet individuals like Alex Toth have actually currently won it.
I have actually checked out the secret individuals have made use of to win the lotto.
Due to this, I am sharing with you this secret information so you can either win the lotto or lose it all.
To calculate the expected value of gain or loss, you need to consider the probability of each outcome and the corresponding payoff.
In this case, there are two possible outcomes:
1. Winning the jackpot with a probability of 1 in 13,983,816.
2. Losing and not winning the jackpot with a probability of 1 - 1/13,983,816 (complement of the winning probability).
The payoff for winning the jackpot is $1 million, and the cost of buying a ticket is $2.
To calculate the expected value, you multiply each outcome by its corresponding probability and sum them up. Let's calculate it step by step:
1. Calculate the probability of winning the jackpot:
Probability of winning the jackpot = 1 / 13,983,816.
2. Calculate the probability of losing:
Probability of losing = 1 - (1 / 13,983,816).
3. Calculate the expected value:
Expected value = (Probability of winning * Payoff) + (Probability of losing * Cost)
Expected value = (1 / 13,983,816) * $1,000,000 + (1 - (1 / 13,983,816)) * (-$2)
Now, let's calculate the expected value:
Expected value = (1 / 13,983,816) * $1,000,000 + (1 - (1 / 13,983,816)) * (-$2)
Expected value ≈ $0.0715 - $0.00000014285
Expected value ≈ $0.0715
Therefore, the expected value of gain or loss for buying one ticket in this scenario is approximately $0.0715. This means, on average, you can expect to gain $0.0715 every time you play Lotto 6/49 with a $2 ticket.