A television station would like to decide between extending a current television show for another season or develop a completely new show for that time slot.

It will cost $6M to develop the new show. The new show may be very successful, moderately successful, or not successful with associated advertising revenues of $25M, $15M, or $5M, respectively.

If the station chooses to extend the current show, it will cost $2M. The extended show may be very successful, moderately successful, or not successful with associated advertising revenues of $15M, $10M, or $5M, respectively.

Suppose that the probabilities associated with show success are changed so that both shows are set at 0.2, 0.5, and 0.3, for very successful, moderately successful, and not successful outcomes, respectively.

Which of the following are true?

Question

A television station would like to decide between extending a current television show for another season or develop a completely new show for that time slot.

It will cost $6M to develop the new show.  The new show may be very successful, moderately successful, or not successful with associated advertising revenues of $25M, $15M, or $5M, respectively.

If the station chooses to extend the current show, it will cost $2M.  The extended show may be very successful, moderately successful, or not successful with associated advertising revenues of $15M, $10M, or $5M, respectively.

Suppose that the probabilities associated with show success are changed so that both shows are set at 0.2, 0.5, and 0.3, for very successful, moderately successful, and not successful outcomes, respectively.

Which of the following are true?

BlackTom AI · Accepted Answer

We start by restating the scenario and the options to keep track of what we are evaluating.

Question scenario: A TV station must choose between developing a new show (cost 6M) with possible net revenues of 19M, 9M, or -1M for very successful, moderately successful, and not successful respectively, given probabilities 0.2, 0.5, 0.3. Alternatively, extending the current show costs 2M and yields net revenues of 13M, 8M, or 3M for the same outcome levels and probabilities. We compute EMV (expected monetary value) for each option:

- New show: net outcomes per scenario are 25-6 = 19, 15-6 = 9, 5-6 = -1. EMV = 0.2*(19) + 0.5*(9) + 0.3*(-1) = 3.8 + 4.5 - 0.3 = 8.0 (million).
- Extended show: net outcomes per scenario are 15-2 = 13, 10-2 = 8, 5-2 = 3. EMV = 0.2*(13) + 0.5*(8) + 0.3*(3) = 2.6 + 4.0 + 0.9 = 7.5 (million).

Now we evaluate each answer choice:

Option 1: "The EMV of the decision to develop the new show is $10.0M." This is incorrect because the calculated EMV for the new show is 8.0, not 10.0. The miscalculation could stem from misapplying the revenues or mis-weighting probabilities, but the correct weighted sum with the given net outcomes yields 8.0.

Option 2: "The EMV of the decision to extend the existing show is $8.0M." This statement is false since the EMV for extending the existing show is 7.5, not 8.0. A common pitfall is rounding or incorrectly computing one of the scenario net values, but with net values 13, 8, and 3 and the given probabilities, the weighted sum is 7.5.

Option 3: "A best decision is to choose the existing show." This claim is unsupported by the numbers because the EMV for the new show is higher (8.0 vs 7.5). The term "best" would typically refer to the option with the higher EMV, so here the new show would be the preferred choice if we are selecting by EMV.

Option 4: "The EMV of the decision tree is $8.5M." Here the statement asserts a single EMV for the whole decision tree of 8.5. However, the separate EMVs for the two choices are 8.0 (new) and 7.5 (extend); there is no single EMV of 8.5 that corresponds to the decision tree under these numbers, so this is incorrect.

Option 5: "Exactly two answers are correct." Given the calculations above, none of options 1–4 match the computed EMVs or the recommended decision. Therefore, this meta-statement is not supported by the computations we performed.

Option 6: "None of the answers are correct." This statement would be evaluating the entire set of options 1–5. Since we found that 1–4 do not match the calculated EMVs or the implied recommendation, and 5 is a claim about the count of correct statements rather than a numerical EMV, option 6 aligns with the notion that the prior options do not accurately reflect the computed results. Note that the exact interpretation depends on whether one treats option 6 as claiming all previous options are incorrect; the calculations shown demonstrate that the EMV values are 8.0 for the new show and 7.5 for the extension, which undercuts options 1–4, while option 5’s claim about “two correct answers” is not supported by the computed EMVs.

In summary, the numeric computations yield EMV_new = 8.0 and EMV_extend = 7.5, and the first four statements do not match these figures. The final option asserts none of the earlier statements are correct, which corresponds to the alignment with the calculated results. The key ideas to internalize are how to compute EMV as a probability-weighted average of net outcomes and how to compare EMVs across alternatives to identify the implicit recommended choice.

MGMT 101 LEC ONL: MANA... Study Checkpoint 8: Decision Analysis I

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