The television production company ZVTV Productions has developed

Question

‎‎ ‎ ‎ ‎ ‎ ‎The television production company ZVTV Productions has developed a script for a pilot episode of a new television series called Whatsit. The following gives information about all the costs and revenues that would arise, depending on the decisions made.

‎‎ ‎ ‎ ‎ ‎ ‎The cost of the script development, in Hong Kong dollars, was HK$ 100,000. The rival production company Vidrama has offered to buy the script and all the intellectual-property (IP) rights for the series from ZVTV Productions for HK$800,000, its final offer.

‎‎ ‎ ‎ ‎ ‎ ‎ZVTV Productions could reject Vidrama's offer, spend HK$400,000 to produce the pilot episode, and try to sell the IP rights for the series to the television network Teevisio. If Teevisio accepted the pilot, they would pay HK$2,000,000 to acquire all the IP rights for the script, pilot, and series. However, if Teevisio rejected the pilot, neither Vidrama nor any other company would buy any of the IP rights mentioned.

‎‎ ‎ ‎ ‎ ‎ ‎Before deciding whether to accept Vidrama's offer, ZVTV Productions could pay the consulting firm Critico to evaluate Whatsit and assess the likelihood that Teevisio would buy all the IP rights for the script, pilot, and series. Critico would charge HK$100,000.

callingTardis · Accepted Answer

Q2: only 500K loss is possible among the 3 options. attaching an image to support it. https://gmatclub.com/forum/download/file.php?id=83288 GMAT-Club-Forum-6ic6rpd3.png

TOBEATHATPERSON · Answer

1. For each of the following questions shown on the decision tree and indicating one or more decision points, select Yes if the information provided suggests that the decision(s) involved would be made by Teevisio. Otherwise, select No.

decision(s) involved made by Teevisio
Only Teevisio -> If Teevisio accepted the pilot, they would pay HK$2,000,000 to acquire all the IP rights for the script, pilot, and series.

2.For each of the following amounts, select Yes if the information provided suggests that it is the total amount of a possible loss referred to by some "Loss" circle on the decision tree. Otherwise, select No.

Cost of Script -100,000
Vidrama +800,000
Produce the pilot episode -400,000
Teeviso pay (script, pilot, series) +2,000,000
Critico charge -100,000

In decision tree, there is only these type loss

Hire Critico -> Produce Pilot ==> 500,000
Produce Pilot ==> 400,000

Answer is 500,000 only

3. Suppose that Critico is hired, provides a positive evaluation of the script for Whatsit, and predicts that Teevisio will purchase all the IP rights for the series. If ZVTV Productions then produces the pilot episode, which one of the following is the probability, according to Ms. Chen’s estimates and the other information provided, that Critico’s prediction will NOT be correct?

-> Critico assess the likelihood that Teevisio would buy all the IP rights for the script, pilot, and series. 
-> NOT be correct => not buy 
-> in the decision tree 20 / (80 + 20) = 20%

Bunuel · Answer

Question 2:

A “Loss” circle happens only on paths where ZVTV produces the pilot and then Teevisio does not buy the IP rights. The prompt says that if Teevisio rejects, nobody buys any IP rights, so revenue is zero on those paths. So the loss amount at a “Loss” circle is just total costs paid on that path.

Costs that can be on a path:

Script development: HK$100,000 (already spent no matter what) 
 Pilot production: HK$400,000 (only if they produce the pilot) 
 Critico: HK$100,000 (only if they hire Critico)

Every “Loss” circle is after “Produce pilot,” so every loss includes at least:
HK$100,000 + HK$400,000 = HK$500,000

If they also hired Critico and still produced the pilot and got rejected, the loss would be:
HK$100,000 + HK$100,000 + HK$400,000 = HK$600,000.

Now the three amounts:
 
 HK$100,000: No. Any loss must include the HK$400,000 pilot cost too, so it cannot be only HK$100,000. 
 HK$500,000: Yes. This is the loss when they do not hire Critico, produce the pilot, and Teevisio rejects. 
 HK$800,000: No. Maximum loss is HK$600,000.

akhilsundar422 · Answer

For the second one: why is 100000 of script making not considered?

SomeOneUnique · Answer

akhilsundar422 
Rergarding Q2, if we consider the rightmost branch of the decision tree, the loss incurred is as follows:
-Develop script : HK$ 100,000
-Hire Critico->NO : HK$ 0
-Sell script to Vidrama->NO : HK$ 0
-Produce Pilot : HK$ 400,000
-All rights purchased->NO : All in vain, nobody would buy any IP rights.
-----------------------------------------------------------------------------------------------
Total loss = HK$ 100,000 + HK$ 400,000 = HK$ 500,000

Thus, YES only for option B(HK$ 500,000) and NO for the other 2 parts.

kk166 · Answer

ZVTV Productions has developed a script for a TV pilot episode called  Whatsit . They have several options on how to proceed:

Sell the script and IP rights to Vidrama for HK$800,000 . 
  Produce the pilot themselves and then try to sell the IP rights to a television network like Teevisio . If Teevisio buys the IP rights, they would pay HK$2,000,000.  
Before making these decisions, ZVTV could hire Critico, a consulting firm, to evaluate the likelihood that Teevisio would buy the IP rights. Critico charges HK$100,000 for this evaluation.

Decision Tree Breakdown:

The decision tree you provided shows all the possible decisions and outcomes that ZVTV Productions can face. Let's break down some key parts:

First Decision: Hire Critico?

ZVTV Productions needs to decide whether to hire Critico to evaluate the script. This is a decision made by ZVTV, not Teevisio.   
  Second Decision: Positive Evaluation of Script?

If ZVTV hires Critico, they will receive an evaluation of the script's potential. The outcome of this evaluation (positive or negative) helps ZVTV decide the next steps. This evaluation is conducted by Critico, not Teevisio. 
  Note:  Teevisio has no involvement in the evaluation process, so the decision here is not made by Teevisio.   
  Third Decision: Sell Script to Vidrama?

ZVTV can decide to sell the script to Vidrama, regardless of whether they hired Critico. Again, this is a decision made by ZVTV, not Teevisio.   
  Fourth Decision: Produce Pilot?

If ZVTV decides not to sell the script to Vidrama, they can produce the pilot themselves. This decision is also made by ZVTV.   
  Fifth Decision: All IP Rights Purchased?

After producing the pilot, ZVTV will attempt to sell the IP rights. Whether or not the IP rights are purchased depends on the decision made by Teevisio or another potential buyer. 
  Here, Teevisio (or another buyer) would decide whether to purchase all the IP rights.  Therefore, this decision is made by Teevisio.    
 Questions Answered:

All IP rights purchased?

Yes,  this decision is made by Teevisio (or another potential buyer). 
 Explanation: After ZVTV produces the pilot, it’s up to Teevisio to decide whether they want to buy all the IP rights. If Teevisio decides to purchase them, they pay HK$2,000,000. If not, ZVTV incurs a loss. This is Teevisio's decision.   
  Positive evaluation of script?

No,  this decision is not made by Teevisio. 
 Explanation: This decision is about whether Critico evaluates the script positively. This evaluation is internal to ZVTV and Critico; Teevisio is not involved.   
  Sell script to Vidrama?

No,  this decision is not made by Teevisio. 
 Explanation: This decision is made by ZVTV. They can choose to accept or reject Vidrama’s offer to buy the script and IP rights. Teevisio does not influence this decision.

sanyuktabhattad · Answer

Can someone please explain Q3?

maheshdrag · Answer

Probability of A when B is P(A)*P(B). Consider the question. Lets first ignore the not and focus on the probability of being true.

Normally, it would be 60% of 80% for a +ve evaluation and acquisition of the IP. In this case, it is given that the probability of a positive evaluation is 100% because it is stated as a premise in the question.

In this case, the expected +ve eval is 100% of 80% = 80%. Now let's bring back the not from the Original Q stem. Probability that this is untrue = 100% - 80% = 20%

egmat · Answer

Question 3:

The earlier replies from maheshdrag and TOBEATHATPERSON both landed on  20% , and the key is seeing  which  node on the tree the question is actually asking about.

Let me anchor to the  Options tab  decision tree. The question hands you a specific path as already-decided:

- Critico  is  hired - so we're on the "yes, Hire Critico" branch.
- The evaluation  is  positive - so we take the " 60%  yes" (positive evaluation) branch.
- ZVTV  does  produce the pilot.

That lands you at the node  "All IP rights purchased?"  with  80%  yes /  20%  no.

What the prediction is, and when it's wrong

Critico's prediction is:  Teevisio will purchase all the IP rights.  On the tree, "purchased" is the  80%  branch. So the prediction is  correct80%  of the time and  NOT correct  the remaining  20%  - that's answer  B .

The one thing to be careful about

The trap here is wanting to also multiply by the  60%  (positive evaluation) probability and get something like  0.6  x  0.8 .  Don't.  The question already  tells you  the evaluation came back positive - that event has happened, so its probability is no longer in play. You're working  inside  the positive-evaluation branch, where the only relevant split is the  80 / 20  node. The prediction fails exactly on the  20%  "no" side.

Think of it like this: if I tell you "the coin already landed heads, now I roll a die - what's the chance it's not a  6 ?" you just answer  5/6 . You don't re-multiply by the coin's probability, because that part is given. Same move here: positive evaluation is given, so only the  20%  matters.

Answer: B

Rickooreo · Answer

Given that in the question 3 - 80+20% both adds up to 100% thus we are not solving as conditional probability ?

What would have been the solution like if it didn't add up to 100%

would it have been 20/(80+20) where value for 20 and 80 will change based on the values provided ?

egmat · Answer

Hi Rickooreo,

Great instinct to poke at  why  it's just  20% . Let me separate the two things going on, because your  20 /( 80 + 20 ) is actually hiding the real insight.

Why the 80 and 20 always sum to 100%

On the  Options tab  decision tree, the node "All IP rights purchased?" has exactly two branches:  80% yes  and  20% no . Those are the  only  two things that can happen at that node - Teevisio either buys or doesn't. So they  must  sum to  100% . This isn't a lucky coincidence for this problem;  every  decision node's branches cover all outcomes at that point, so they always total  100% .

That's why your  20 /( 80 + 20 ) collapses to  20 / 100  =  20% . At a single node, the "conditional" version and the plain version give the same number - there's no scenario at one node where the branches sum to something  other  than  100% .

Where conditioning actually happens here

The genuine conditional move in this question isn't at the  80 / 20  node - it's the  60%  you correctly left out. Normally the chance of "positive evaluation  and  purchase" would be  0.60  x  0.80 . But the stem  hands you  "Critico provides a positive evaluation" as already true. Once that event is given, you're locked inside the positive-evaluation branch, and its  60%  drops out of the math. What's left is only the  80 / 20  split, and "prediction NOT correct" = the  20% no  side. That's answer  B .

So to answer your "what if it didn't add to  100% ": at a single decision node it always will. You'd only ever divide by a partial total if you were combining  across  nodes with some outcomes excluded - but this question isolates one node, so the answer is simply the  20%  branch.

Answer: B

Moriarty017 · Answer

Hi Bunuel, Shouldn't the rejected offer of 800k from Vidrama also be included in all the losses, if not then why?

Bunuel · Answer

The HK$800,000 is  not a loss because ZVTV never had or paid that money . It was only an offer they rejected. The “Loss” circles include only the money ZVTV actually spent.

Suni18 · Answer

Hi @Bunel,

Won't the script production also considered a loss?

Bunuel · Answer

Yes, the HK$100,000 script development cost  is part of the loss .

But it is not the  entire  loss. Every path that ends in a “Loss” circle also includes the HK$400,000 pilot cost.

So the minimum total loss is:

HK$100,000 + HK$400,000 =  HK$500,000 .

arunbhati · Answer

Hi  Bunuel ,

I don't understand the solution of Q3. can you please explain me from basics

Bunuel · Answer

Question 2:

The question is asking:
 
Given that Critico gave a positive evaluation and predicted that Teevisio would buy the IP rights, what is the chance that this prediction turns out to be wrong?