Statistics and Probability
Chance and probability
Say how likely an event is, and write its probability as a fraction.
Some things are certain, some are impossible, and most sit somewhere in between. Probability puts a number on that. It runs from 0 for something that cannot happen to 1 for something that must happen, and everything else lands between the two.
The rule for equally likely outcomes
When every outcome is equally likely, the probability of an event is the number of outcomes you want divided by the total number of outcomes. The word 'fair' in a question is what promises you that the outcomes really are equally likely — a loaded die or a weighted coin would break the rule.
Have a play
Every chance there is sits somewhere on this line, from impossible at one end to certain at the other. Move along it.
Tap anywhere on the line.
Worked example
A bag holds 3 red, 4 blue and 5 green marbles. What is the probability of drawing a blue one?
Count all the outcomes: 3 + 4 + 5 = 12 marbles.
The total goes on the bottom, and the commonest mistake in the whole topic is using the wrong total — 4 out of 8, say, forgetting that the blues belong in the total too.
Try it together
Now let us work one out together: a bag holds 7 white counters and 3 black counters.
Total first, then the ones you want, then the fraction. And a probability that comes out above 1 always means a slip somewhere.
1.How many counters are in the bag altogether?
Have a go
Have a go on your own: a spinner has 5 equal sections numbered 1 to 5. What is the probability of landing on an odd number? Write your answer as a fraction.
Hint: Count how many of the five numbers are odd.
Ready to practice?
Eight questions on what you have just read. Nothing is timed, and you can play as many times as you like.