The probability that an event will occur is the proportion of times the event is expected to happen in a suitably large experiment.

A set of events are exhaustive if at least one of them has to occur whenever the experiment is carried out.

Mutually exclusive events have no outcomes in common.

Venn diagrams are a representation used to model statistical/probability questions. Commonly circles are used to represent events.

Advanced problem solving with conditional probability

Maths

Checking and securing displaying outcomes

Checking and securing exhaustive events

Probabilities involving algebra

Frequency trees

Checking and securing calculating probabilities from tables

Checking and securing calculating probabilities from diagrams

Experimental probability

Experimental vs theoretical probability

Set notation

Conditional probability in a two-way table

Conditional probability in a Venn diagram

Conditional probability in a tree diagram

Algebra in tree and Venn diagrams

Constructing three event Venn diagrams

Probabilities in three event Venn diagrams

Comparing multiple representations to calculate conditional probabilities

Combinations

In this unit, pupils use their knowledge of calculating theoretical probabilities and extend this understanding to calculating conditional probabilities using all of the representations encountered in the prior unit.

In this unit, pupils use their knowledge of calculating theoretical probabilities and extend it to calculate conditional probabilities.

Conditional probability

Which diagram is most appropriate to use to solve the following problem: A bag contains 12 blue and 8 red counters. Two counters are taken at random. What is the probability that they are both red?

A bag contains 12 blue counters and 8 red counters. Two counters are taken at random (without replacement). What is the probability that they are both red?

Each of these spinners is spun once. Find P(the sum of the outcomes is greater than 5).

Each of these spinners is spun once. Find P(the sum of the outcomes is 4 given B lands on 2).

A bag contains only red counters and blue counters. Jun picks two counters at random from the bag. The tree diagram shows some probabilities. There were {{ }} counters in the bag at the start.

There are $$n$$ cards in a pack. 6 of the cards are black cards and the rest are red. Sam draws two cards at random from the pack. There were {{ }} cards in the pack at the start.

There are 5 children sat around one table and 6 children sat around another table. The teacher chooses 1 child from each table. In how many different ways could the teacher do this?

Here is a restaurant menu for three courses.  A customer can choose one starter and one main course in {{ }} different ways.

Here is a restaurant menu for three courses.  A customer can choose one main course and one dessert in {{ }} different ways.

Alex has a pack of 7 cards. He deals one card to himself and deals one card to Sam. In how many different ways can this happen?

Izzy has a pack of 5 cards. She takes 2 cards at random from the pack. In how many different ways can this happen?

Alex draws 2 different cards from set A and 2 different cards from set B. There are {{ }} different ways are there of doing this.

Exit Quiz

Which diagram is most appropriate to use to solve the following problem: A bag contains 12 blue and 8 red counters. Two counters are taken at random. What is the probability that they are both red?