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Probability questions as counting problems
This article examines how probability can often be viewed simply as counting the number of ways certain events can occur, before covering some summarising examples.
problem
Worked example: counters in bags
Age
16 to 18
Challenge level
This worked example computes the number of ways we can move counters around in two bags to determine a probability of interest.
problem
Teams
Age
16 to 18
Challenge level
Two brothers belong to a club with 10 members. Four are selected
for a match. Find the probability that both brothers are selected.
problem
How many balls?
Age
16 to 18
Challenge level
A bag contains red and blue balls. You are told the probabilities
of drawing certain combinations of balls. Find how many red and how
many blue balls there are in the bag.
problem
Rain or shine
Age
16 to 18
Challenge level
Predict future weather using the probability that tomorrow is wet
given today is wet and the probability that tomorrow is wet given
that today is dry.
problem
Fa cup
Age
16 to 18
Challenge level
In four years 2001 to 2004 Arsenal have been drawn against Chelsea
in the FA cup and have beaten Chelsea every time. What was the
probability of this? Lots of fractions in the calculations!
article
Raffles and strings
How much are you likely to win from a raffle? How many loops will you make with some strings? Here, two guided examples can be found for you to work through.
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Prepare for university - pure mathematics
Helpful preparation for those intending to study a course involving pure mathematics at university.
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Prepare for university - applied mathematics
Helpful preparation for university for those intending to study a
course involving applied mathematics at university.
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NRICH and Olympiads
A useful entry point into the NRICH site for those students interested in Mathematical Olympiad problems or the Maths Challenges.