Probability

Probability compares the total number of outcomes you want to the total number of outcomes.

Assume we are flipping a coin and we want heads.

You have probably already guessed that the probability is half or 50%. We write this as 0.5 because later it will make the math more convenient to have 1 represent “all” or “the total of everything”.

For the coin flip problem–heads or tails–we knew enough information to calculate the probablility of heads. What if we didn’t know enough and we had to determine the probability by experiment?

We could flip the coin ‘x’ number of times and let ‘h’ be the number of times that the result was heads.

After a lot of flips done by a hunan, we might end up with some answer like 0.47 and we might get 0.4995 if we had a robot do it a lot more times.

This is the brief introduction version–you will want more. It’s in the oven and will come out soon.

Appendix A

What is the probability of rolling two dice and getting a pair of sixes?

Even though the rolls are done at the same time, we consider this problem to be two rolls. When you want to calculate the probability two events and you know thr probability for each event, you multiply the two probabilities.

The probability a single six roll is 1 / 6.

The pronability of two six rolls is 1/36.

Now, change the question to the following: What is the probability of rolling a 5 or 6 when rolling a six sided die once?

For this question the two probabilities add. The probability of a five is 1/6 and the probability of a six is 1/6. The probability of getting one or the other is 2 / 6 or 1 / 3.