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### Number and algebra

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### Advanced mathematics

# Advanced Problem Solving Module 16

### Probability Questions as Counting Problems

### Worked Example: Counters in Bags

### Teams

### How Many Balls?

### Rain or Shine

### FA Cup

### Raffles and Strings

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Age 16 to 18

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.

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.

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.

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.

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.

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!

Age 16 to 18

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.