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To cover quantum phenomena, we need to first remind ourselves of 'classical' probabilities. In this sense, 'classical' just means pre-quantum, i.e. the normal probability trees you should have seen in school. If you're already familiar with this material, you should move through it quickly. If you're not so hot on this then don't worry- we'll only cover some of the simplest probability problems possible.

You will hopefully remember probability trees from school. The idea is simple - we use a drawing to map out every possible eventuality and from this, we can calculate the chance of it happening.

Say we have a coin, and to start, we place it in the state Heads. If we then toss this fair coin and look at it, there is a 50% chance we will see Heads again, and a 50% chance of seeing Tails instead. We can plot this on a probability tree like so:

We draw the outcomes on the end of each branch, and the probabilities of each occurrence on the branches. Similarly, if we started in the state Tails and tossed the coin, we would have a 50% chance of seeing Heads and a 50% chance of seeing tails.

We can test this works by trying it. You can physically get a coin out, flip it many times, and record each result; you will eventually see roughly 50% of your results are Heads and 50% tails. Around 500 to 1000 tosses should be enough to get reliable results.

Too lazy to try this? Dont worry! You can simulate the coin-tossing experiment by pressing the Toss Coin button below to simulate a coin toss and store the results. You can change the initial state to 'Heads' or 'Tails', or increase the number of coins (No. of Coins) slider to get many results quickly. Click Reset to discard your results and start again.

The rest is here:

What is Quantum? - Qiskit