If this spinner is spun once, what is the probability of not getting a vowel? Give your answer as a fraction.
So first of all, we’re actually gonna look at a key word within this question, which is “not”. They’re actually being very kind in this question and written in capitals, but make sure, because it’s a very common mistake, that if you see a “not” in there, you take this into consideration as it makes a big difference for what we’re actually looking for.
So we’re looking for the probability of not getting a vowel. So if we want to find out the probability of not getting a vowel, a good place to start would be what are the vowels. Well, the vowels are actually A, E, I, O, and U. So let’s take a look and see how many of those we’ve actually got within our spinner.
So if we take a look at our spinner, we actually have A, I, and U. So we actually have three vowels. And therefore, we have B, F, H, and G which aren’t vowels. So we have four nonvowels. So now we know how many vowels and nonvowels we have. We can actually find out the probability of not getting a vowel. And we can actually find that probability because we know that the probability of an event, or I’ve written here is 𝑃 event, is equal to the number of event outcomes divided by the total possible outcomes.
So therefore the probability of not getting a vowel is gonna be equal to four, because that’s the number of nonvowels, over three plus four, cause I’ve just done this stage because what that is is that’s going to be our total number of outcomes because there are actually seven different sections on our spinner.
So therefore, we can say that the probability of not getting a vowel is equal to four over seven. And that’s because we had four nonvowels over a total number of outcomes, which was seven because there are seven actual spaces on our spinner. It’s actually worth mentioning at this point a common mistake.
A common mistake would be to get the answer four over three, and this is where people have actually just had a look and they’ve gone, “Right, we’ve got four nonvowels, great! Oh and there’s three vowels. We’ll put that as our denominator.” But that would give us the incorrect answer. So just beware of that when you come across this kind of question.