The Monty Hall Problem Demonstrates the Challenge of Assessing Probabilities

Probability calculations are tricky and subtle changes in context can make all the difference in the outcome. I was reminded of this recently when setting up BrainTwister #10. New Scientist That’s roughly the probability that two pairs of people can sit next to each other on 22 chairs.

Several readers emailed me to say that my solution was wrong. I came up with all the possible seating arrangements and counted the ones where two groups were next to each other. Meanwhile, readers counted the ways they could have one group sit first and then the second group sit next to each other. Neither approach was wrong, depending on how they sat.