there will be a coin toss to determine the winner of the $5 million prize. You are offered $100,000 for your ticket right now. What would you do?
I would keep it. The chances of winning the toss is 50%. Whereas, if I sold my ticket, the chances of winning are 0%. You're welcome. - Wrinkly
To make a decision, it's important to consider the odds and personal preferences. Let's break down the potential outcomes and consider the expected value of each choice:
1. Keeping the ticket:
If you keep the ticket and participate in the coin toss, there are two possible outcomes: heads or tails. If you win, you'll receive the $5 million prize; if you lose, you won't receive anything.
The expected value of this choice can be calculated as follows:
(Expected Value) = (Probability of Winning) * (Value of Winning) + (Probability of Losing) * (Value of Losing)
(Expected Value) = (0.5) * ($5 million) + (0.5) * ($0)
Therefore, the expected value of keeping the ticket is $2.5 million.
2. Selling the ticket:
If you sell the ticket for $100,000, you'll have that amount guaranteed regardless of the coin toss outcome. This option eliminates the risk factor associated with the coin toss.
Based on the expected value analysis, if you believe that having a guaranteed $100,000 is more valuable to you than the potential risk and reward of participating in the coin toss, it may be more logical to sell the ticket.
However, it's important to consider personal preferences, risk tolerance, financial needs, and the individual value placed on the thrill of taking a chance. These subjective factors should also be taken into account when making a decision in such situations.