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answer explaination
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Hi officiisnobis,

Yes, you've got both right: 80 for the first blank and 90 for the second. Here's the reasoning so it clicks.

The key move is Marcus's one rule: every product-quality complaint must also involve delivery. So look at Elena's diagram and find the only two product-quality regions that don't touch the Delivery circle:

- Billing ∩ Product quality = 8% (the 8% lens between Billing and Product quality, outside Delivery)
- Product quality only = 5% (the 5% at the bottom)

Marcus slides each of these into Delivery:

- The 8% joins the center - all-three region becomes 12 + 8 = 20%
- The 5% joins Delivery ∩ Product quality - 17 + 5 = 22%

Everything else stays as Elena had it.

Blank 1 - billing that also involves delivery

All billing complaints: Billing only 10 + Billing ∩ Delivery 20 + all three 20 = 50%.

Billing and delivery: Billing ∩ Delivery 20 + all three 20 = 40%.

Therefore the fraction is 40 / 50 = 80%. Note the base here is billing complaints (50%), not all complaints - that's the spot that trips people up.

Blank 2 - all complaints involving delivery

Add every region inside the Delivery circle after Marcus's shift:

- Delivery only 28
- Billing ∩ Delivery 20
- All three 20
- Delivery ∩ Product quality 22

Total = 90%.

So 80% and 90% are correct. The whole question hinges on remembering to move both delivery-free product-quality regions (the 8% and the 5%) before you count.

Answer: 80

officiisnobis
is it first blank - 80 and second blank - 90?
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