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Year 11

Foundation

Problem solving with conditional probability

I can use my knowledge of conditional probability to solve problems.

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New

Year 11

Foundation

Problem solving with conditional probability

I can use my knowledge of conditional probability to solve problems.

Download all resources

Share activities with pupils

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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
A clear, logical, structured argument is much easier to follow and understand

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.

Common misconception

Pupils may represent probabilities in the wrong position on the probability scale by miscounting the number of intervals required.

Before using any probability scale, it can be helpful to make a note of the sizes for each major and minor interval.

Pupils will find this lesson easier if they are already confident with converting between fractions, decimals, percentages and ratios.

Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Starter quiz

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6 Questions

Q1.

Mutually __________ events have no outcomes in common.

conditional

Correct answer: exclusive

inclusive

independent

Q2.

Sofia has to catch a bus and then a train to get to school. When the bus is late, Sofia is more likely to miss the train and so be late for school. Match each value to its probability.

Correct Answer:$$x$$,0.2

0.2

Correct Answer:$$y$$,0.25

0.25

Correct Answer:$$z$$,0.9

0.9

Q3.

Sofia has to catch a bus and then a train to get to school. When the bus is late, Sofia is more likely to miss the train and so be late for school. P(Sofia is late for school) = .

Correct Answer: 0.22

Q4.

Here is a general probability tree. Which of these probabilities give the probability of the highlighted events?

Correct answer: P(A ∩ C)

P(A ∪ C)

Correct answer: P(A) × P(C | A)

P(A) × P(A | C)

P(C) × P(A | C)

Q5.

One marble is taken at random from a bag of 7 purple and 5 green marbles. The marble is not replaced. A second marble is then taken. The tree diagram shows these two events. Find the value of $$z$$.

$$7 \over 12$$

$$5 \over 12$$

Correct answer: $$7 \over 11$$

$$6 \over 11$$

$$5 \over 11$$

Q6.

One marble is taken at random from a bag of purple and green marbles. The marble is not replaced. A second marble is then taken. The tree diagram shows the two events. Find P(both marbles are purple).

$$\frac{49}{132}$$

$$\frac{49}{144}$$

$$\frac{9}{22}$$

Correct answer: $$\frac{7}{22}$$

$$\frac{5}{33}$$

Exit quiz

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6 Questions

Q1.

Starting with the least likely, put these probabilities in order of likelihood.

1 - $$0.2$$

2 - $$3\over10$$

3 - $$35$$%

4 - $$0.42$$

5 - $$9\over20$$

6 - 48%

Q2.

The probability of three outcomes to a trial are shown in the table. The outcomes are exhaustive and mutually exclusive. Find P(C).

Correct answer: $$10$$%

$$15$$%

$$20$$%

$$\frac{1}{5}$$

Correct answer: $$\frac{1}{10}$$

Q3.

Jacob and Sofia each play a tennis match. Find the probability that both Jacob and Sofia win their match.

$$ \frac{1}{5}$$

$$ \frac{2}{5}$$

Correct answer: $$ \frac{3}{5}$$

$$ \frac{4}{5}$$

Q4.

Jacob and Sofia each play a tennis match. Find the probability that at least one of them wins their match.

Correct answer: $$\frac{19}{20}$$

$$\frac{18}{20}$$

$$\frac{17}{20}$$

$$\frac{16}{20}$$

$$\frac{15}{20}$$

Q5.

A box contains green and blue marbles. Some of the marbles have swirls on them. The Venn diagram shows the number of each type. P(B) = . Give your answer as a decimal.

Correct Answer: 0.4, 0.40

Q6.

A box contains green and blue marbles. Some of the marbles have swirls on them. The Venn diagram shows the number of each type. P(S ∪ B) = . Give your answer as a decimal.

Correct Answer: 0.76