The expected value is calculated as a long-run average by weighting each net outcome by its probability. First, determine the net profit for winning and losing.
Conditions: The lottery has three positions with ten choices each, allowing repetition.; The model assumes all 1000 ordered tickets are equally likely.; The ticket costs $1.; The winning prize payment is $500, which includes the full prize amount.
The expected value is calculated as a long-run average by weighting each net outcome by its probability. First, determine the net profit for winning and losing.
Conditions: The lottery has three positions with ten choices each, allowing repetition.; The model assumes all 1000 ordered tickets are equally likely.; The ticket costs $1.; The winning prize payment is $500, which includes the full prize amount.
Expected profit is a long-run average calculated by weighting outcomes by their probabilities. It does not guarantee that any single trial or even a finite series of trials will yield exactly that amount, because actual results vary randomly around the mean.
Conditions: The scenario involves random outcomes with assigned probabilities.; The calculation uses the probability-weighted average (expectation).
Expected profit is a long-run average calculated by weighting outcomes by their probabilities. It does not guarantee that any single trial or even a finite series of trials will yield exactly that amount, because actual results vary randomly around the mean.
Conditions: The scenario involves random outcomes with assigned probabilities.; The calculation uses the probability-weighted average (expectation).
The expected value of -$0.50 should be interpreted as a long-run average loss per ticket, not as a guaranteed result for a single play. In any individual game, the player will either win $499 or lose $1; the -$0.50 figure represents the mean outcome if the game were played many times.
Conditions: The expected value has been calculated as -$0.50.; The context involves understanding the meaning of expectation in probability.
The expected value of -$0.50 should be interpreted as a long-run average loss per ticket, not as a guaranteed result for a single play. In any individual game, the player will either win $499 or lose $1; the -$0.50 figure represents the mean outcome if the game were played many times.
Conditions: The expected value has been calculated as -$0.50.; The context involves understanding the meaning of expectation in probability.