Advanced problem solving with conditional probability | Maths

Starter quiz

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?

11

22

15

30 ✓

60
Here is a restaurant menu for three courses. A customer can choose one starter and one main course in ______ different ways.

'12' ✓
Here is a restaurant menu for three courses. A customer can choose one main course and one dessert in ______ different ways.

'6' ✓
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?

13

14

21

36

42 ✓
Izzy has a pack of 5 cards. She takes 2 cards at random from the pack. In how many different ways can this happen?

9

10 ✓

16

20

25
Alex draws 2 different cards from set A and 2 different cards from set B. There are ______ different ways are there of doing this.

'216' ✓

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?

tree diagram ✓

two-way table

Venn diagram
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?

$\frac{56}{400}$

$\frac{64}{400}$

$\frac{56}{380}$ ✓

$\frac{64}{380}$
Each of these spinners is spun once. Find P(the sum of the outcomes is greater than 5).

$6 \over 24$

$8 \over 24$ ✓

$9 \over 24$

$10 \over 24$

$11 \over 24$
Each of these spinners is spun once. Find P(the sum of the outcomes is 4 given B lands on 2).

$1\over2$

$1\over3$

$1\over4$ ✓

$1\over5$

$1\over6$
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.

'25' ✓
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.

'15' ✓

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Lesson Details

Key learning points

Probabilities may appear in unfamiliar contexts
Probabilities may require a strong knowledge of converting between fractions, decimals and percentages
Selecting an appropriate and efficient method for solving the problem comes from evaluating methods
The preferred representation may change depending on the context

Common misconception

Pupils may think that only one type of diagram/table can be used to solve each probability problem, or be unsure which representation to use when it is not provided to them.

Probability problems can often be modelled using multiple types of representation. The one you choose may depend on the information that you are trying to organise and what you then intend to do with that information.

Keywords

Probability - The probability that an event will occur is the proportion of times the event is expected to happen in a suitably large experiment.
Exhaustive events - A set of events are exhaustive if at least one of them has to occur whenever the experiment is carried out.
Mutually exclusive - Mutually exclusive events have no outcomes in common.
Venn diagram - Venn diagrams are a representation used to model statistical/probability questions. Commonly circles are used to represent events.