Analyze decisions and strategies using probability concepts in more complex settings.
Find the net expected value by weighting outcomes and then including a fixed cost
Problem
What is the net expected value after including the fixed cost: a \(\$5\) game pays \(\$20\) with probability \(0.2\) and \(\$0\) otherwise?
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What this problem is really about
Separate the random payout from the fixed cost so neither is counted incorrectly. First average the possible payouts with their probabilities, then subtract the cost that occurs on every play exactly once. An equivalent check is to convert every branch to a net payoff before weighting; both setups should produce the same long-run net value.
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