# Video: AF5P3-Q01-585146572179

What is the probability of rolling an odd number on an ordinary fair dice? Circle Your answer. 1/6, 2/6, 6/1, 1/2.

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### Video Transcript

What is the probability of rolling an odd number on an ordinary fair dice? Circle Your answer.

Well, for this question, what we’re trying to do is work out the theoretical probability of rolling an odd number on an ordinary fair dice. And it’s theoretical because we’re not doing any trials, we’re not experimenting by rolling the dice, we’re just calculating the probability. And to work out theoretical probability, what it’s equal to is the number of desired outcomes, so in this case the number of odd numbers, divided by the total number of possible outcomes, so in this case the total number of numbers on our dice.

So therefore, we can say the probability of an odd number, and I’ve used probability notation here, so we’ve got 𝑃 then a bracket with odd inside. And this is gonna be equal to, well, it’s gonna be equal to the number of desired outcomes to the number of odd numbers. Well, if we look at the numbers on an ordinary dice, we’ve got one, two, three, four, five, six. So, we’ve got three odd numbers cause we got one, three, and five. So, that’s gonna be three. And this is gonna be over the total number of possible outcomes. We’ll consider there are six possible outcomes because, as we’ve already said, it’s one, two, three, four, five, or six. So therefore, we could say the probability of rolling an odd number on an ordinary fair dice is three over six.

But hold on. Three over six is not one of the answers. So, what do we need to do now? Well, we need to simplify our fraction. And to simplify our fraction, one way of doing this is by looking at the numerator and denominator and finding a common factor, in fact the highest common factor. And we can see that the highest common factor of three and six is three.

So, we divide the numerator and denominator by three, which is gonna give us one-half, or one over two. And that’s because three divided by three is one, and six divided by three is two. We also could’ve seen that it was gonna be a half because three is half of six. So therefore, we can say that the probability of rolling an odd number on an ordinary fair dice is a half. And I have circled the fourth answer, which is our correct answer.