Subject: Follow-Up Request: Heating Repair

Dear [Landlord’s Name],

I hope you’re well. I’m writing to follow up on the heating issue in [apartment address/unit number], which I first reported on [date]. The heating has now been out for three weeks.

I understand that repairs can sometimes take time, but this has become urgent. Please arrange for the heating to be repaired as soon as possible and let me know the date and time a technician will attend.

I value having a good relationship and appreciate your prompt attention to this. I’m simply asking for the repair to be completed without further delay.

Thank you, [Your Full Name] [Your Phone Number] [Your Email Address]

import { useEffect, useRef, useState } from "react";

/**
 * Returns a debounced version of `value`.
 * - Updates only after `delay` ms have passed without changes.
 * - Cleans up pending timers on value/delay change and on unmount.
 */
export function useDebouncedValue<T>(value: T, delay: number): T {
  const [debouncedValue, setDebouncedValue] = useState<T>(value);
  const timeoutRef = useRef<ReturnType<typeof setTimeout> | null>(null);

  useEffect(() => {
    // Clear any existing timer before scheduling a new one
    if (timeoutRef.current) {
      clearTimeout(timeoutRef.current);
    }

    timeoutRef.current = setTimeout(() => {
      setDebouncedValue(value);
      timeoutRef.current = null;
    }, delay);

    // Cleanup runs on dependency change and unmount
    return () => {
      if (timeoutRef.current) {
        clearTimeout(timeoutRef.current);
        timeoutRef.current = null;
      }
    };
  }, [value, delay]);

  return debouncedValue;
}

Example usage

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

export function SearchBox() {
  const [query, setQuery] = useState("");
  const debouncedQuery = useDebouncedValue(query, 400);

  // Use debouncedQuery for API calls, filtering, etc.
  // e.g. useEffect(() => fetchResults(debouncedQuery), [debouncedQuery]);

  return (
    <input
      value={query}
      onChange={(e) => setQuery(e.target.value)}
      placeholder="Type to search..."
    />
  );
}

Use Bayes’ theorem.

Let:

• (D): person uses the drug

• (\neg D): person does not use

• (+): test is positive

Given “99% accurate,” we’ll interpret as:

• (P(+\mid D)=0.99) (sensitivity)

• (P(-\mid \neg D)=0.99) so (P(+\mid \neg D)=0.01) (false positive rate)

• (P(D)=0.005) (0.5% prevalence), so (P(\neg D)=0.995)

Then

[ P(D\mid +)=\frac{P(+\mid D)P(D)}{P(+\mid D)P(D)+P(+\mid \neg D)P(\neg D)} ]

[ =\frac{0.99\cdot 0.005}{0.99\cdot 0.005+0.01\cdot 0.995} =\frac{0.00495}{0.0149} \approx 0.332 ]

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

Why this surprises people

People often focus on “99% accurate” and assume a positive means ~99% chance of true use. But because usage is very rare (0.5%), false positives from the large non-user group are numerous enough to dominate many positives. This is the base rate effect (or base rate neglect).

Quick intuition with 100,000 people:

• Users: 500 → true positives: (0.99\times500=495)

• Non-users: 99,500 → false positives: (0.01\times99{,}500=995)

Total positives (=495+995=1490), and true users among them (=495), so (495/1490\approx 33\%).