3.12

# Independent but non-identical events

In this and the next two steps, we will complete our learning journey by presenting examples of more complex problems in probability.

This step will continue our work from the previous one, by looking at questions that involve events that are not identical, but are still independent. The next two steps will cover:

• Two dependent events

• Inverse conditional probability (Bayes’ Theorem)

We will then provide all of the solutions to the sample questions, as well as a further opportunity to discuss classroom approaches.

We will start with non-identical independent events. This is a simple extension of the type of situation that we looked at in the previous step; although the second event may be of a completely different type to the first, the events are still independent and the product rule can be used to find the probabilities of outcomes. The example questions should make it clear how this works.

## Sample examination-style questions

### Question 1

Nadiyah has three coins in her pocket: 5p, 10p, and 50p. Alexander also has three coins in his pocket: one 10p and two 20p coins. A packet of sweets is 30p.

• If each person takes a single coin at random from their pocket, what is the probability that together they will have enough to buy a packet of sweets?

### Question 2

Mona is going on a gap year and buys travel insurance for theft and illness. The probability that she will be robbed is 0.1, and the probability that she falls ill is 0.2. These events are independent of each other.

• What is the probability that she will need to make any claim on her insurance?

• Out of 100 similar travellers, how many would you expect to make claims for both being robbed and falling ill?

Use the comments to share your solutions and any reflections on the material covered here.