Transcript
NARRATOR:
What is probability? Probability gives us a way of measuring or assessing uncertainty. It measures the likelihood of certain random events. We're going to go through some examples.
Take a 6-sided dice. What's the probability that we'll throw a 3? We know that there are 6 possible outcomes: 1, 2, 3, 4, 5, and 6. But there's only one 3. And so there's a 1 in 6 chance, or a 1 in 6 probability, of rolling number 3. We would express that probability as 1 divided by 6, which is 0.167.
Taking the same 6-sided dice, what's the probability that we'll throw an even number? Well, there's 3 even numbers on a dice: 2, 4, and 6, and there's 6 possible outcomes, so we'd express this as 3 over 6, which is a half, or 0.5.
What's the probability that we'll throw an even number greater than 3? There are 2 even numbers greater than 3: 4 and 6. So there's 2 numbers and 6 possible outcomes. So the probability here is 2 out of 6, which is one third, or 0.33. We can see that probability compares the number of times the desired outcome happens with the total number of possible outcomes.
What's the probability that you'll throw an odd number greater than 3? The answer here is 1 in 6 because there's only 1 odd number greater than 3 - that's 5. And so we say there's a 1 out of 6 probability.
What's the probability that we'll throw a number greater than 3? Well, there are 3 numbers greater than 3: 4, 5, and 6. So we would immediately think it's 3 out of 6, which is 0.5.
But another way of doing this is to say, what's the probability of throwing even numbers greater than 3, and adding that to the probability of throwing odd numbers greater than 3. And so the probability of throwing a number greater than 3 should equal the probability of throwing the even numbers plus the probability of throwing the odd numbers.
Here, we've got the probability of throwing an even number greater than 3 as 0.333 and the probability of throwing an odd number greater than 3 as 0.167. If you add them together, it's 0.5. This only works because they're what we call mutually exclusive events. A number greater than 3 cannot be both odd and even.
So each of the numbers: 4, 5, and 6 can only be an even number or an odd number. And when you have mutually exclusive events, you can do this adding up calculation. So one way of calculating the probability of an outcome is to compare the number of ways that outcome may occur with the total number of possible outcomes.