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# Combining Probabilities

**Keywords:**Energy and Entropy, Probability, Eigenstates, Small Group Activity

### Highlights of the activity

- This small group activity is designed to help students understand how to combine probabilities in non-interacting systems.
- Students calculate the probability, for two uncorrelated systems A and B, of system A being in state i and system B being in state j, given the probabilities for each independent system.
- The wrap-up discussion reinforces the concept that probabilities are multiplied, and introduces the mathematical notation used to describe probabilities.

### Reasons to spend class time on the activity

Many students at this point in their educational career have not had much experience with statistical mechanics in thermodynamic systems. This activity is an excellent introduction to probabilities in quantum mechanical systems. This activity also provides a good exercise for students to see how probabilities of non-dependent systems interact.