Transcript

NARRATOR:

Let's throw 2 6-sided die. What's the probability that you'll throw a total equal to 7? Remember what we need to do. We're going to compare the number of times it could happen with the total number of complete possibilities.

Here's all the complete possibilities. There are 36 ways that the two die could fall. Out of these, how many ways are there of getting 7? I've put them all in red. There's 6 possible ways or 6 combinations. So 6 over 36, which is the same as one sixth, which is 0.167.

What's the probability of throwing first a 2 and then an even number greater than 3? Well, let's start with the first die. Throwing a 2, we know happens 1 out of 6 times. There's only one 2, and there's 6 outcomes. This means that anything which comes after, whatever that probability, is only going to happen one sixth of the time. So it's going to be whatever this probability is times one sixth.

The second throw, throwing an even number greater than 3, is going to happen 2 out of 6 times. But the first row is only happening one sixth of the time. Therefore, the second throw can only happen one sixth of its normal probability. And so we multiply two sixths, which is actually one third, by one sixth to get two thirty-sixths, or one eighteenth. So events that follow each other can be multiplied by the individual probabilities.

Here's some overall rules about probability. The probability of all possible outcomes has to equal 1. What's the probability of throwing an odd number? 3 over 6. What's the probability of throwing an even number? 3 out of 6. In other words, the probability of everything happening is 1.

For combined mutually exclusive events, we can add probabilities. We looked at mutually exclusive events in example 5. Combined events - one dice, then another - can be found by multiplying their probabilities. And of course, if something doesn't have a possibility of it happening, we can still use the rule of how often it happens compared to the total. So if the number of times it happens is 0, then the probability must be 0.

And finally, before we leave the intrinsic approach, we can also use history, studies, or market research to come up with probabilities. Here's something from a medical piece of research. 2619 men were found to have certain risk factors to do with coronary heart disease. Of those men, at the end of the 8-year study, 246 of them had suffered with heart disease.

So if the total possible men that could have coronary heart disease with a risk factor is 2619 but only 246 went on to actually get it, then the probability of getting it is this figure here. The number of those who did over the total number who could have. So 246 over 2619. In other words, a probability of 0.094.