This is part of our collection of Short Problems.
You may also be interested in our longer problems on Probability - Stage 4.
Printable worksheets containing selections of these problems are available here
Tying the Rope
What is the probability that two pieces of rope are tied together, when Pat ties two loose ends together?
Collecting Marbles
How many marbles need to be taken out to ensure that at least three are of the same colour?
Swapping Sweets
If two girls each take a sweet from each other's bags, what is the probability that they end up with what they started with?
Flipping Coins
A coin is flipped 4 times. What is the probability of getting heads at least 3 times?
Odd Dice
These strange dice are rolled. What is the probability that the sum obtained is an odd number?
One or Both
Problem 1 was solved by 70% of the pupils. Problem 2 was solved by 60% of them. Can you work out how many pupils took the exam?
Takeaway Time
Pizza, Indian or Chinese takeaway? If everyone liked at least one, how many only liked Indian?
Switch On
In how many different ways can a row of five "on/off" switches be set so that no two adjacent switches are in the "off" position?
XOXOXO
6 tiles are placed in a row. What is the probability that no two adjacent tiles have the same letter on them?
CD Collection
How many different ways can I arrange the CDs in my collection?
Dropouts
What percentage of students who graduate have never been to France?
Gambling at Monte Carlo
A man went to Monte Carlo to try and make his fortune. Is his strategy a winning one?
Different Digital Clock
At how many times between 10 and 11 o'clock are all six digits on a digital clock different?
Medal Ceremony
The teacher has forgotten which pupil won which medal. In how many different ways could he give the medals out to the pupils?
Descending Deal
Four cards from a set numbered 1-36 are dealt. What is the probability that they are dealt in order?
Two Girls
There are 10 girls in a mixed class. If two pupils are selected, the probability that they are both girls is 0.15. How many boys are in the class?
Phone Call
How many different phone numbers are there starting with a 3 and with at most two different digits?
Vegtown Elections
What percentage of people voted for the Broccoli party in the Vegtown election?
Counting Kangaroos
Can you work out how many kangaroos Rachel draws in one colour?
Numbers or Letters?
Which game offers you the best chance of winning?
Domino Match
If you take two dominoes from a set at random, what is the probability that they 'match'?