The OR rule
Sometimes we want to know the probability of getting one result or another. The OR rule can help us here if the two results are mutually exclusive.
Mutually exclusive means that the two outcomes of the same event cannot happen at the same time. The outcome of a football match is an example of something that is mutually exclusive as the match is either won, lost or drawn, it cannot be both won and drawn at the same time.
A second example is rolling a dice, getting a 6 or a 3. As the outcome cannot be both 6 and 3 these events are mutually exclusive. This would not be true of rolling a dice and getting a 6 or an even number, as both of these events could occur together because 6 is also even.
When events are mutually exclusive and we want to know the probability of getting one event OR another, then we can use the OR rule.
Example
Jane is wondering what she is going to have for tea when she gets home. She estimates that there is a \(\frac{1}{10}\) chance that her parents will make her stew and a \(\frac{1}{5}\) chance that they will make her lasagne. What is the probability she would get stew or lasagne?
Solution
Using the OR rule P(stew or lasagne) = P(stew) or P(lasagne).
P(stew or lasagne) = \(\frac{1}{10}\) + \(\frac{1}{5}\)
To add these fractions we must realise that \(\frac{1}{5} = \frac{2}{10}\)
\(\frac{1}{10} + \frac{2}{10} = \frac{3}{10}\)
Question
Ashley is going to roll a dice. What is the probability he will get an odd number or a two?
Using the OR rule. P(odd or two) = P(odd) + P(two).
P(odd) = \(\frac{3}{6}\) and P(two) = \(\frac{1}{6}\).
P(odd or two) = \(\frac{1}{6}\) + \(\frac{3}{6}\) = \(\frac{4}{6}\).
Question
Geraldine is going to roll a dice and flip a coin. She wants to know the probability that she will get either a 2 or a head. She says that the probability of this happening is \(\frac{4}{6}\). Explain why she is wrong.
Using the OR rule P(2 or head) = \(\frac{1}{2} + \frac{1}{6} = \frac{3}{6} + \frac{1}{6} = \frac{4}{6}\).
This could then be simplified to \(\frac{2}{3}\).
However, the OR rule cannot be used here because the events are not mutually exclusive. We know this because it is possible to get a head and a two.
