the organizers can expect to take in $64,000. Since it costs$50,000 to stage the event, this translates to a profit of $14,000, so they should certainly go ahead with the venture. It's important to realize that none of the outcomes actually produces an amount of$64,000. This is simply the weighted average of all possible outcomes. Although there is a 50% chance of a loss the big profit that will be made the remaining 50% of the time more than offsets this and creates an overall expected profit.

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Subject 6. Expected Value, Variance, and Standard Deviation of a Random Variable
is likely to be profitable. Using the expected value formula, we will multiply each amount by its probability, and add the answers. E(X) = 200,000 x 0.2 + 80,000 x 0.3 + 0 x 0.5 = 40,000 + 24,000 + 0 = $64,000 Thus, <span>the organizers can expect to take in$64,000. Since it costs $50,000 to stage the event, this translates to a profit of$14,000, so they should certainly go ahead with the venture. It's important to realize that none of the outcomes actually produces an amount of \$64,000. This is simply the weighted average of all possible outcomes. Although there is a 50% chance of a loss the big profit that will be made the remaining 50% of the time more than offsets this and creates an overall expected profit. However, with a one-off concert, there is a major risk involved, particularly in the event of unfavorable weather. An easier way to interpret expected value is as follows: