# Advanced Problem Solving Module 16

## Advanced Problem Solving Module 16

### Probability Questions as Counting Problems

##### Stage: 5

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.

### Worked Example: Counters in Bags

##### Stage: 5 Challenge Level:

This worked example computes the number of ways we can move counters around in two bags to determine a probability of interest.

### Teams

##### Stage: 5 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.

### How Many Balls?

##### Stage: 5 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.

### Rain or Shine

##### Stage: 5 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.

### FA Cup

##### Stage: 5 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!

### Raffles and Strings

##### Stage: 5

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.