Probability tricky exercise

Question

I was given this exercise:

The manager of a company has 2 possible designs for his new line of artificial brains. The first option has an 80% of probability of producing 70% of the artificial brains in good conditions and a 20% of probabilities of producing 50% of the artificial brains in good conditions, being 450000 dollars the cost of these designs. The second option has a 70% of probability of producing 70% of the artificial brains in good conditions and a 30% of probabilities of producing 50% of the artificial brains in good conditions, being 600000 dollars the cost of this design. The cost of each artifical brain is 100 dollars, it if is good its cost is 250 dollars while if it is in bad condition it has no price. Knowing that the vision on the compay is to create 50000 artificial brains, which design must be chosen by the manager?

I did this but im not sure

Option 1:

80% * 70% * 50,000 = 2,800,000 good artificial brains
20% * 50% * 50,000 = 500,000 good artificial brains
Total good artificial brains: 3,300,000
Total cost: $450,000
Total revenue: 3,300,000 * $250 = $825,000,000
Expected profit: $825,000,000 - $450,000 = $824,550,000
Option 2:

70% * 70% * 50,000 = 2,450,000 good artificial brains
30% * 50% * 50,000 = 750,000 good artificial brains
Total good artificial brains: 3,200,000
Total cost: $600,000
Total revenue: 3,200,000 * $250 = $800,000,000
Expected profit: $800,000,000 - $600,000 = $799,400,000

Therefore, based on these calculations, the manager should choose Option 1

Is my reasoning okay?

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edit #1

Option 1:

80% * 70% * 50,000 = 2,800,000 good artificial brains
20% * 50% * 50,000 = 500,000 good artificial brains
Total good artificial brains: 3,300,000
Total cost: $450,000
Total revenue: 3,300,000 * $250 = $825,000,000
Expected profit: $825,000,000 - $450,000 = $824,550,000
Option 2:

70% * 70% * 50,000 = 2,450,000 good artificial brains
30% * 50% * 50,000 = 750,000 good artificial brains
Total good artificial brains: 3,200,000
Total cost: $600,000
Total revenue: 3,200,000 * $250 = $800,000,000
Expected profit: $800,000,000 - $600,000 = $799,400,000

Therefore, based on these calculations, the manager should choose option 1

Answer 1

I'm still not sure how to reconcile the "cost of each artificial brain is 100 dollars" with the rest of the information given, but in the absence of a better explanation I'm going to assume that the cost of designing the two brains is \$450,000 and \$600,000 respectively, while the cost of manufacturing the brains is \$100 apiece.

You must be aware that $80\% = \frac{80}{100} = 0.8 \neq 80$; to calculate $80\%$ of $70\%$ of $50,000$, the multiplication would be $(0.8)(0.7)(50,000) = 28,000$. So your option 1 calculations should be as follows:

• $80\%$ of $70\%$ of $50,000 = (0.8)(0.7)(50,000) = 28,000$ good artificial brains
• $20\%$ of $50\%$ of $50,000 = (0.2)(0.5)(50,000) = 5,000$ good artificial brains
• Total good artificial brains: $33,000$
• Total cost: $\$450,000 + 33,000 (\$100) = \$3,750,000$
• Total revenue: $33,000 (\$250) = \$8,250,000$
• Expected profit: $\$8,250,000 - \$3,750,000 = \$4,500,000$

The option 2 calculations should be similar.