Video: Determining the Probability of Union of Two Events in a Spinner Experiment

A spinner has 10 equal sections labeled from 1 to 10. Determine the probability of the pointer landing on 4 or 7.

02:33

Video Transcript

A spinner has 10 equal sections labeled from one to 10. Determine the probability of the pointer landing on four or seven.

So when we look at this question, there’s actually one keyword and it’s very small word. But the word is “or” cause we’re looking for the probability of the pointer landing on four or seven. And we’re just gonna have a look at why this word “or” is actually useful in this kind of question because we’re gonna take a quick look at the And and Or rules — a couple of rules that we use when we’re dealing with probability.

So what the first rule tells us — so the And rule — it tells us that if we have two events, the probability of A and B occurring is equal to the probability of A multiplied by the probability B, whereas our Or rule actually tells us that if we have the probability of A or the probability of B, then this is gonna be equal to the probability of A plus the probability of B.

As we’ve already discussed, we actually have an “or” in this question. So therefore, it’s the second rule that we’re gonna be using. I’m gonna use it to help us find out the value of the probability of the pointer landing on a four or a seven. Well, the first thing we need to do before we can actually work out the probability of landing on a four or a seven is actually work out the probability of each individual event — so the probability of a four and the probability of a seven.

Well, if we take a look at the question, it says that we have 10 equal sections. And if you have 10 equal sections, then it means that each section is as equally as likely to be landed on. So therefore, the probability that they’re gonna land on a four is one over 10. And therefore, because as we said before, everything is as equally likely to happen in the probability of landing on seven. So therefore, we’re gonna have one over 10 as well for the probability of seven.

So great, so now, we’ve got the probability of four and the probability of seven. What we need to do is work out what the probability of landing on a four or a seven is. Well, from our Or rule, we know that the probability of a four or a seven is gonna be equal to the probability of four plus the probability of seven, which is gonna be equal to one-tenth plus one-tenth which gives us an answer of two tenths because when we’re adding fractions with the same denominator, we just add the numerators.

Okay, so we got two tenths. And therefore, if we cancel this down by actually dividing the numerator and the denominator by two because it’s a factor of both, we can therefore say that the probability of the pointer landing on a four or a seven is gonna be equal to one-fifth.

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