Conditional probability in a two-way table | Maths | Quizalize & Oak National Academy

Starter quiz

Which symbol is used to represent the union of two sets?

A

A'

ξ

∪ ✓

∩
What does this symbol represent: ' ?

complement ✓

element

intersection

union

universal set
What region is shown shaded in this Venn diagram?

A' ∩ B

A ∩ B′

A' ∪ B′

A ∪ B′ ✓

A' ∪ B
ξ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}, A = {multiples of 4}, B = {factors of 12}. Find P(A' ∩ B').

$\frac{3}{12}$

$\frac{4}{12}$

$\frac{5}{12}$ ✓

$\frac{6}{12}$

$\frac{7}{12}$
Which combination of events is highlighted in the tree diagram?

A' ∩ B'

A' ∩ B ✓

A ∩ B'

A' ∪ B

A ∪ B'
Lucas and Izzy each play one game of chess that they can either win or lose. P(Lucas wins ∩ Izzy wins) = ______ (give your answer as a decimal).

'0.45' ✓

Exit quiz

The probability of an outcome occurring given that another event has occurred is called ______ probability.

'conditional' ✓
Select the example of events which are not independent.

Taking a marble at random from a bag, replacing it and then taking another

Taking a marble at random from a bag, keeping it and then taking another ✓

Rolling two dice together

Rolling a dice and a flipping a coin
The table shows the types of marble in a bag. Match each event to its probability.

P(blue)

⇔

$28\over 60$ ✓

P(green)

⇔

$32\over 60$ ✓

P(blue and has no swirl)

⇔

$11\over 60$ ✓

P(blue given it has no swirl)

⇔

$11\over 27$ ✓

P(green and has a swirl)

⇔

$16\over 60$ ✓

P(green given it has swirl)

⇔

$16\over 33$ ✓
A marble is taken at random from a box of blue and green marbles. Alex works out that P(swirl and blue) = 0. This shows the event 'taking a blue marble' and the event 'taking a swirl marble' are...

conditional.

exhaustive.

independent.

mutually exclusive. ✓
A 20-sided die with integers from 1 to 20 written on it is rolled once. Select the pair of mutually exclusive events.

A factor of 18

A factor of 15 ✓

Even number ✓

Odd number

Prime number
A deck of cards has a number on it (either prime or non-prime), and a symbol (a circle, square, or wave). A card is selected at random from the deck. Find P(square | prime).

$13 \over 21$

$13 \over 31$ ✓

$21 \over 31$

$21 \over 56$

$31 \over 56$

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Lesson Details

Key learning points

A two-way table can be used to calculate conditional probabilities
A two-way table can be used to calculate conditional probabilities involving sets of events
Two-way tables allow us to identify which events are mutually exclusive
Two-way tables can be used to identify which events are independent

Common misconception

Pupils may conflate the meaning of mutually exclusive with the meaning of independent.

Emphasise the word 'exclusive' in 'mutually exclusive' to suggest that one event excludes the other. Also, emphasise that the opposite of independent is dependent.

Keywords

Conditional probability - Conditional probability is the probability of an outcome occurring given that another event has occurred.
Mutually exclusive - Mutually exclusive events have no outcomes in common.
Independent events - Event A is independent of event B if the probability of event A occurring is not affected by whether or not event B occurs.