Question

The chance of winning a lottery game is

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t in approximately 27 million. Suppose you buy a $1 lottery ticket in anticipation of winning the $7 million grand prize. Calculate your ex.

Answer 1

The expected value (EV) of buying a $1 lottery ticket with a 1 in 27 million chance of winning a $7 million grand prize is approximately -$0.74.

Step-by-step explanation:

The expected value (EV) of an action, in this case, buying a lottery ticket, is calculated by multiplying the probability of each outcome by the respective payoff and summing these values. In this scenario, the probability of winning is 1 in 27 million, and the potential prize is $7 million. The formula for expected value (EV) is given by:

EV=(Probability of Winning×Prize if Win)−Cost of Ticket.

Substituting the values:

`\[EV = ((1)/(27,000,000) * $7,000,000) - $1\]`

`\[EV \approx $0.259 - $1\]`

`\[EV \approx -$0.741.\]`

A negative expected value indicates that, on average, buying a lottery ticket results in a financial loss. In this case, for every $1 spent on a ticket, the expected return is -$0.74. This is expected, given the long odds of winning. While individual experiences may vary, the collective average over many attempts converges to this negative value, making the lottery a statistically unfavorable investment. It's essential for individuals to understand the probabilistic nature of lotteries and approach them as a form of entertainment rather than a reliable means of financial gain.