# The Prisoner Problem

Explore a simpler version of the Prisoner Problem as featured in Matt's video. What's the probability that the prisoners will survive? What is it that makes their strategy a good one?
Age groups relevant for by Key Stage:
KS3,
KS4,
KS5
30 mins - 1 hour,
1 hour – 2 hours

## Curriculum Topics Covered

Permutations, Probability.

The puzzle in these activities is a simpler version of the Prisoner Problem featured in Matt's video.

In Matt's video there are 10 prisoners and 10 cabinets and cards, whereas we have only 4 of everything. We give students the prisoners' strategy and ask the question 'What is the probability that the prisoners survive using their strategy?'

We find that there is a 42% chance that the prisoners will survive if they use their strategy. This is amazing! If the prisoners were choosing randomly and independently of each other, they would each have a half chance of getting their card, and therefore they would be a one in sixteen chance of them all getting their cards and surviving.