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
problem
Tying the rope
Age
14 to 16
Challenge level
What is the probability that two pieces of rope are tied together, when Pat ties two loose ends together?
problem
Collecting marbles
Age
14 to 16
Challenge level
How many marbles need to be taken out to ensure that at least three are of the same colour?
problem
Swapping sweets
Age
14 to 16
Challenge level
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?
problem
Flipping coins
Age
14 to 16
Challenge level
A coin is flipped 4 times. What is the probability of getting heads at least 3 times?
problem
One or both
Age
14 to 16
Challenge level
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?
problem
Takeaway time
Age
14 to 16
Challenge level
Pizza, Indian or Chinese takeaway? If everyone liked at least one, how many only liked Indian?
problem
Switch on
Age
14 to 16
Challenge level
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?
problem
XOXOXO
Age
14 to 16
Challenge level
6 tiles are placed in a row. What is the probability that no two adjacent tiles have the same letter on them?
problem
CD collection
Age
14 to 16
Challenge level
How many different ways can I arrange the CDs in my collection?
problem
Odd dice
Age
14 to 16
Challenge level
These strange dice are rolled. What is the probability that the sum obtained is an odd number?
problem
Different digital clock
Age
14 to 16
Challenge level
At how many times between 10 and 11 o'clock are all six digits on a digital clock different?
problem
Medal ceremony
Age
14 to 16
Challenge level
The teacher has forgotten which pupil won which medal. In how many different ways could he give the medals out to the pupils?
problem
Descending deal
Age
14 to 16
Challenge level
Four cards from a set numbered 1-36 are dealt. What is the probability that they are dealt in order?
problem
Two girls
Age
14 to 16
Challenge level
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?
problem
Phone call
Age
14 to 16
Challenge level
How many different phone numbers are there starting with a 3 and with at most two different digits?
problem
Vegtown elections
Age
14 to 16
Challenge level
What percentage of people voted for the Broccoli party in the Vegtown election?
problem
Counting kangaroos
Age
14 to 16
Challenge level
Can you work out how many kangaroos Rachel draws in one colour?
problem
Numbers or letters?
Age
14 to 16
Challenge level
Which game offers you the best chance of winning?
problem
Domino match
Age
14 to 16
Challenge level
If you take two dominoes from a set at random, what is the probability that they 'match'?
problem
Dropouts
Age
14 to 16
Challenge level
What percentage of students who graduate have never been to France?