Problem solving with conditional probability | Maths | Quizalize & Oak National Academy

Starter quiz

Mutually __________ events have no outcomes in common.

conditional

exclusive ✓

inclusive

independent
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.

$x$

⇔

0.2 ✓

$y$

⇔

0.25 ✓

$z$

⇔

0.9 ✓
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) = ______.

'0.22' ✓
Here is a general probability tree. Which of these probabilities give the probability of the highlighted events?

P(A ∩ C) ✓

P(A ∪ C)

P(A) × P(C | A) ✓

P(A) × P(A | C)

P(C) × P(A | C)
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 $z$ .

$7 \over 12$

$5 \over 12$

$7 \over 11$ ✓

$6 \over 11$

$5 \over 11$
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).

$\frac{49}{132}$

$\frac{49}{144}$

$\frac{9}{22}$

$\frac{7}{22}$ ✓

$\frac{5}{33}$

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

$10$ % ✓

$15$ %

$20$ %

$\frac{1}{5}$

$\frac{1}{10}$ ✓
Jacob and Sofia each play a tennis match. Find the probability that both Jacob and Sofia win their match.

$\frac{1}{5}$

$\frac{2}{5}$

$\frac{3}{5}$ ✓

$\frac{4}{5}$
Jacob and Sofia each play a tennis match. Find the probability that at least one of them wins their match.

$\frac{19}{20}$ ✓

$\frac{18}{20}$

$\frac{17}{20}$

$\frac{16}{20}$

$\frac{15}{20}$
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.

'0.4' ✓
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.

'0.76' ✓

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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

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.

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.