Subject: Urgent: Heating repair needed

Dear [Landlord/Property Manager’s Name],

I hope you’re well. I’m writing to follow up on the heating issue at [address/unit number], which I first reported on [date]. It has now been three weeks, and the heating is still not working properly.

I understand that repairs can sometimes take time, but the lack of heat is making it difficult to comfortably and safely use the home, especially given the weather. I would appreciate it if you could arrange for the repair to be completed as soon as possible.

Could you please let me know by [specific date, e.g., the end of the week] what the next step will be and when a repair person will attend? If there is a delay, please also let me know the reason and the expected timeline.

I’d like to resolve this quickly and amicably, and I’m happy to cooperate with access or scheduling if needed. Please let me know if you need anything further from me.

Thank you for your attention to this matter.

Best regards, [Your Name] [Phone Number] [Address/Unit Number]

import { useEffect, useState } from "react";

export function useDebouncedValue<T>(value: T, delayMs: number = 300): T {
  const [debouncedValue, setDebouncedValue] = useState<T>(value);

  useEffect(() => {
    const timeoutId: ReturnType<typeof setTimeout> = setTimeout(() => {
      setDebouncedValue(value);
    }, delayMs);

    // Cancels the pending debounce when:
    // - `value` changes
    // - `delayMs` changes
    // - the component unmounts
    return () => {
      clearTimeout(timeoutId);
    };
  }, [value, delayMs]);

  return debouncedValue;
}

Usage:

import { useState } from "react";
import { useDebouncedValue } from "./useDebouncedValue";

export function SearchInput() {
  const [search, setSearch] = useState("");
  const debouncedSearch = useDebouncedValue(search, 500);

  return (
    <div>
      <input
        value={search}
        onChange={(event) => setSearch(event.target.value)}
      />

      <p>Debounced value: {debouncedSearch}</p>
    </div>
  );
}

Assuming “99% accurate” means:

• 99% sensitivity: a user tests positive with probability 0.99

• 99% specificity: a non-user tests negative with probability 0.99

and the prevalence is 0.5%, then:

[ P(\text{user} \mid \text{positive}) = \frac{P(\text{positive} \mid \text{user})P(\text{user})} {P(\text{positive} \mid \text{user})P(\text{user}) + P(\text{positive} \mid \text{non-user})P(\text{non-user})} ]

[ = \frac{0.99 \times 0.005} {0.99 \times 0.005 + 0.01 \times 0.995} ]

[ = \frac{0.00495}{0.00495 + 0.00995} \approx 0.332 ]

So the probability they actually use the drug is about 33%.

Why this surprises people

People often hear “99% accurate” and think a positive result must mean there is a 99% chance the person uses the drug. But that confuses:

[ P(\text{positive} \mid \text{user}) ]

with:

[ P(\text{user} \mid \text{positive}) ]

The key issue is the base rate: only 0.5% of people use the drug, so there are many more non-users than users. Even a small false-positive rate among the large non-user population creates many false positives.

Natural-frequency explanation

Imagine testing 100,000 people:

• Drug users: [ 0.5\% \times 100{,}000 = 500 ] True positives among users: [ 99\% \times 500 = 495 ]

• Non-users: [ 99{,}500 ] False positives among non-users: [ 1\% \times 99{,}500 = 995 ]

Total positive tests:

[ 495 + 995 = 1{,}490 ]

Of those, actual users are:

[ \frac{495}{1{,}490} \approx 33\% ]

So despite the test being highly accurate, a positive result only implies about a one-in-three chance of actual drug use because the drug is rare in the population. This is a classic example of base-rate neglect.