Probability question

Question

Hello, my question is about probabilities from a game called "Deceit". Here are the premises.

1. 6 players, 2 unknow infected players among them.
2. Each one has therefore 1/3 chance of being infected (2/6).
3. We isolate two random people from the group.
4. From the isolated group of two, ONLY one of the two is guaranteed to be infected.
5. Therefore, the players of the isolated group have 1/2 chance of being infected, and the other group of 4, have 1/4 of being infected, since there is still an unknow infected player among them.
6. After, we bring back the isolated group of 2 to the group of four.

The question is : What are the odds of being infected for EACH and SINGLE player after putting them

back together?

Thank you for your answers!

Answer 1

Brils... let's play!

Initial Scenario:

1. Total players: 6
2. Infected players: 2
3. Chance of being infected initially: 1/3

Isolation Phase:

1. Two people are isolated; one is guaranteed to be infected.
2. Chance of being infected in isolated group: 1/2
3. Chance of being infected in the non-isolated group: 1/4

After Reintegration:

1. Isolated Players:
2. Probability remains 1/2 or 50%. The isolation process confirmed at least one infected individual in this pair, and reintegrating them doesn't change this probability.
3. Non-Isolated Players:
4. Probability remains 1/4 or 25%. The non-isolated group's probability doesn't change upon reintegration because no new information about their infection status is revealed.

Further Exploration:

1. Conditional Probability:
2. Players can use this information to make strategic decisions in the game. Knowing you have a lower chance of being infected if you're not isolated can be advantageous.
3. Strategy Implications:
4. If a player knows they are in the less likely group (1/4 chance), they may choose to be more aggressive in their actions, assuming they are 'safer.'
5. Group Dynamics:
6. The isolated players, knowing they have a higher chance of being infected, might behave more cautiously or deceptively, depending on their actual status.
7. Game Theory:
8. Understanding these probabilities can lead to more complex strategies, including bluffing or double-bluffing based on perceived infection probabilities.
9. Limitations:
10. These probabilities are conditional and based on the rules as stated. They don't account for any additional game mechanics that might reveal more information about who is infected.

I hope this helps. If so, I would greatly appreciate your feedback as I am new to this platform, though very experienced in stats!

Thank you,

Ben