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I think the tag is incorrect because this is clearly math related
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KBoss279
I think the tag is incorrect because this is clearly math related

Updated the tag. Thank you!
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Bunuel


Updated the tag. Thank you!
Hi can you please explain the solution a bit more precisely ..I am unable to follow .. TIA
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Hi,

Let me try to help you with this:

Conditions stated in question:
i) number of units in the order exceeded manufacturing capacity of Plant A (our starting point)
ii) Profit/unit is within $1 of the average (our ending point)

>> Basically we need to find all possible paths from starting -> end point, and then sum them.
As we are looking for simultaneous conditions to exist when going down a particular path (you can think of it as a filtering of a kind), we will multiply.

Path 1: 0.75*0.25 = 0.1875
Path 2: 0.25*0.5 = 0.125

>> This are the correct options for the dropdown respectively. Hope this helps clarify! :)

NupurNeha123

Hi can you please explain the solution a bit more precisely ..I am unable to follow .. TIA
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The difficulty of the problem lies in the "distracting" story of the prompt.
Rest of the solution is just fundamental principle of probability i.e. "AND" means "Multiplication", "OR" means "Addition".
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Hi NupurNeha123,

Happy to break this down step by step!

This question asks: what is the probability that the profit per unit falls WITHIN $1 of the average? Let me walk you through the logic.

Step 1: Understand what 'within $1 of the average' means.
If the average profit per unit is, say, $X, then 'within $1 of the average' means the profit falls in the range from $(X - 1) to $(X + 1). So you need to identify ALL outcomes from the chart that fall inside this range.

Step 2: Read the chart carefully.
The chart shows different profit-per-unit ranges (or outcomes) and their associated probabilities. You need to first locate the average profit per unit — this may be given directly or you may need to calculate it from the distribution shown.

Step 3: Identify which bars/ranges fall within $1 of that average.
Once you know the average, look at the chart and find the ranges that overlap with the interval [average - $1, average + $1]. In this problem, exactly TWO ranges from the chart fall within that $1 window around the average.

Step 4: Add those two probabilities.
The probability for one of those ranges is 0.1875 and the probability for the other is 0.125. Adding them gives: 0.1875 + 0.125 = 0.3125. This is the total probability of being within $1 of the average.

Step 5: Match to the dropdowns.
For D1, the correct choice is 0.1875 (not 0.25 or 0.375). For D2, the correct choice is 0.125 (not 0.5 or 0.0125). Together they complete the sentence: 'the probability... is equal to the sum of 0.1875 and 0.125.'

Key Insight: The key trap here is reading the wrong bars from the chart or miscalculating which ranges fall inside the $1 window. Make sure you are reading the profit values on the correct axis and matching them precisely to the average before selecting which probabilities to add.

Answer: 0.1875, 0.125
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