The OR Rule – Exclusive or Not?

To figure out how to use the OR rule you first need to decide if the events in question can happen at the same time.

For example, can you roll a 6 on a dice and get a heads on a coin? Yes. These events are not mutually exclusive. See the previous post on the AND rule for this.

Mutually exclusive events cannot happen at the same time:

You can’t get a heads and a tails on one toss of the coin.

You can’t roll a 5 and a 6 on one dice roll.

You can’t pass and fail a test.

Great. So what is the OR rule and how do you use it?

The OR rule is this: If you are dealing with mutually exclusive events, and you want to find the probability of at least one of those events happening, then to find the answer, take the probability of each event happening and add them up.

I.e. P(A or B) = P(A)+P(B)

This makes sense, because when you are looking at the chance of different events happening, the probability of at least one of those happening increases.

For example, I have a tin of biscuits. Custard creams, Jammy Dodgers and Chocolate Digestives. (sorry, the first ones that came to mind…probably definitely the ones I ate most in my childhood)

5 Custard Creams

4 Jammy Dodgers

3 Chocolate Digestives

The probability of only picking a custard cream is 5/12.

What is the probablity of picking a Custard Cream or a Jammy Dodger? 5/12 + 4/12 so 9/12.

Hopefully you can see that when you increase the options, it increases the probability.

The And rule is the opposite, it limits the options and so probability decreases by multiplying them together.

Hope that helps!

2 responses

  1. Good explanation! Never heard of those kinds of cookies though. 🙂 Maybe if I ever get to the UK…

    1. You should come, we have the best cookies 🙂

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