Back to topics

Why does switching win more often in Monty Hall?

Three doors hide one prize and two goats. Assume the prize is placed uniformly, and the host knows its location, always reveals a goat behind an unchosen door, and always offers a switch. If two goat doors are available, the host chooses between them equally. Under those rules, switching wins in two of the three possible initial prize placements.

3–7 min

Questions you could explore

  • Why does an uninformed host who happens to reveal a goat create a different problem?

Start reading

Ready to try your ideas aloud?

Your topic carries over. Record up to 2½ minutes, depending on your plan.

Maths and statistics

When one long wait changes the average

An average wait can sound straightforward until one person waits much longer than everyone else. The mean and median offer two ways to summarize that same group. Their different responses to an unusually large value raise a practical question: what do we want an average to tell us?

5–7 min

When one long wait changes the average

Maths and statistics5–7 minAn average wait can sound straightforward until one person waits much longer than everyone else. The mean and median offer two ways to summarize that same group. Their different responses to an unusually large value raise a practical question: what do we want an average to tell us?

Maths and statistics

How is random sampling different from random assignment?

A study can choose people at random, assign them to groups at random, do both, or do neither. Those choices answer different problems: who the findings may describe, and how fairly the study compares conditions.

3–5 min

How is random sampling different from random assignment?

Maths and statistics3–5 minA study can choose people at random, assign them to groups at random, do both, or do neither. Those choices answer different problems: who the findings may describe, and how fairly the study compares conditions.

Why does the Gregorian calendar sometimes skip a leap year?

Maths and statistics2–3 minThe familiar 'every four years' rule has exceptions. The Gregorian calendar treated 1900 and 2000 differently because its century rules refine how calendar years track the solar year.

Why does switching win more often in Monty Hall? | Speech Topic | speaking.app