Probability Explained in 5 Minutes

Probability Explained in 5 Minutes

Probability is part of mathematics, but it's also part of physics. That's because probability talks about what happens when you do an experiment.

Let's do a simple experiment..

We'll toss a coin in the air and see what happens when it hits the ground. It could land heads up, or it could land tails up. It could also land balancing on its edge, but we notice this is extremely rare so we decide to ignore it. So, the experiment has two possible results.

But here's the essential point.. I do the same experiment many times.

I toss the coin in the air n times and I count the number of times it lands heads up, let's call this number h. I notice an interesting thing..

As n increases, h/n seems to approach 0.5, so I can say..

Limit(h/n)=0.5 as n goes to infinity.

So math says this about my experiment..

If I toss a coin just once the "probability" of it landing on heads is 0.5 (50%)

Does this idea help physicists? Yes, big time. They've built probability into the foundations of quantum mechanics. Not all physicists liked this approach and Einstein was a vocal critic. Nevertheless, probability is now a fundamental part of current physical theories.

What happens if I toss a dice? Well, this experiment has 6 possible outcomes, corresponding to the 6 different numbers that can be face up. So, the probability of getting a specific number is 1 out of 6, or 1/6.

Of course, the probability of the outcomes do not have to be equal. If my dice was "loaded" the probability of each number coming up could be different. But one fundamental fact stays the same, the sum of all the probabilities must be 1. So with my loaded dice, if p(m) is the probability of getting m, we have..

p(1)+p(2)+p(3)+p(4)+p(5)+p(6)=1

This just means the probability of something coming up is 1 (100%).

Content written and posted by Ken Abbott abbottsystems@gmail.com