I’ve met a fair number of students who struggle to make sense of probability and it’s usually because of how it has been presented to them.
The main issue is usually the AND rule and the OR rule.
Let’s take a look at the AND rule.
The And rule talks about the probability of lots of different events happening at the same time.
For example, what is the probability of both you and I going somewhere on the weekend?
Very high, right. Most people go somewhere on the weekend, it might be the park, a friend’s house, shopping, a weekend job etc.
What is the probability of both you and I going out to eat on the weekend?
That’s still possible, but less likely than us going somewhere.
What is the probability that both you and I end up in the same restaurant to eat or choosing the same thing to eat?
Again, still possible, but even less likely.
Hopefully you can see that the more events I add in, the probability gets smaller.
All probabilities are given as fractions. When you multiply fractions, they get smaller.
This is why to calculate the probability of independent events happening, the AND rule, tells you to multiply the probability of each event together.
P(A and B) = P(A) x P(B)
What is an independent event?
In probabilty, an independent event is something that is not affected by something that happened before.
For example, if you are rolling a dice, the number you roll is not affected by the number you rolled previously.
If you are rolling a dice and tossing a coin, these are unaffected by what happened previously or by each other.
Dependent events are the kind of activities where you take something and don’t put it back.
For example, the kind of questions where someone is taking coloured counters out of a bag or eating biscuits from a large tin.
The number of counters and biscuits changes each time and this affects the probability each time.
That’s why these events are dependent.