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Year 11
Foundation

Conditional probability in a two-way table

I can calculate a conditional probability from a two-way table.

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New
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Year 11
Foundation

Conditional probability in a two-way table

I can calculate a conditional probability from a two-way table.

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Share activities with pupils
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Lesson details

Key learning points

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

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.

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.

Pupils could be asked to think of other situations where two events are mutually exclusive. They could also think of situations where two events are independent and situations where two events are not independent.
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).

Lesson video

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Starter quiz

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6 Questions

Q1.
Which symbol is used to represent the union of two sets?
A
A'
ξ
Correct answer: ∪
∩
Q2.
What does this symbol represent: ' ?
Correct answer: complement
element
intersection
union
universal set
Q3.
What region is shown shaded in this Venn diagram?
An image in a quiz
A' ∩ B
A ∩ B′
A' ∪ B′
Correct answer: A ∪ B′
A' ∪ B
Q4.
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').
$$\frac{3}{12}$$
$$\frac{4}{12}$$
Correct answer: $$\frac{5}{12}$$
$$\frac{6}{12}$$
$$\frac{7}{12}$$
Q5.
Which combination of events is highlighted in the tree diagram?
An image in a quiz
A' ∩ B'
Correct answer: A' ∩ B
A ∩ B'
A' ∪ B
A ∪ B'
Q6.
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).
An image in a quiz
Correct Answer: 0.45

Exit quiz

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6 Questions

Q1.
The probability of an outcome occurring given that another event has occurred is called probability.
Correct Answer: conditional
Q2.
Select the example of events which are not independent.
Taking a marble at random from a bag, replacing it and then taking another
Correct answer: 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
Q3.
The table shows the types of marble in a bag. Match each event to its probability.
An image in a quiz
Correct Answer:P(blue),$$28\over 60$$

$$28\over 60$$

Correct Answer:P(green),$$32\over 60$$

$$32\over 60$$

Correct Answer:P(blue and has no swirl),$$11\over 60$$

$$11\over 60$$

Correct Answer:P(blue given it has no swirl),$$11\over 27$$

$$11\over 27$$

Correct Answer:P(green and has a swirl),$$16\over 60$$

$$16\over 60$$

Correct Answer:P(green given it has swirl),$$16\over 33$$

$$16\over 33$$

Q4.
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.
Correct answer: mutually exclusive.
Q5.
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
Correct answer: A factor of 15
Correct answer: Even number
Odd number
Prime number
Q6.
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).
An image in a quiz
$$13 \over 21$$
Correct answer: $$13 \over 31$$
$$21 \over 31$$
$$21 \over 56$$
$$31 \over 56$$