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Probabilities involving algebra
I can work with algebraic statements using the fact that exhaustive events sum to 1.
Lesson 3 of 18
New
New
- Year 11
Probabilities involving algebra
I can work with algebraic statements using the fact that exhaustive events sum to 1.
Lesson details
Key learning points
- Equations can be constructed when there is a known relationship between the probabilities of exhaustive events
- Equations can be manipulated and solved to find missing probabilities
- Algebraic statements can be created regardless of the way the probabilities are displayed
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.
Common misconception
Pupils may be unsure whether a variable represents a probability, frequency or a particular outcome.
Variables can be used to represent either of these pieces of information. It can be helpful to start a problem by writing down what any variables represent (e.g. "Let x = the total number of marbles).
Pupils will find this lesson easier if they are already confident with solving linear equations involving algebraic fractions.
Teacher tip
Licence
This content is © Oak National Academy Limited (2025), 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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Prior knowledge starter quiz
6 Questions
Q1.Here are two decks of cards.
A single card from Deck 1 and a single card from Deck 2 is drawn to make a pair.
There are possible outcomes for drawing one card from each deck.
Here are two decks of cards.
A single card from Deck 1 and a single card from Deck 2 is drawn to make a pair.
There are possible outcomes for drawing one card from each deck.
Correct Answer: 16
16
Q2.Here are two decks of cards. A single card from Deck 1 and a single card from Deck 2 is drawn to make a pair.
What is the probability that this pair of cards contains an odd number?
Here are two decks of cards. A single card from Deck 1 and a single card from Deck 2 is drawn to make a pair.
What is the probability that this pair of cards contains an odd number?
$$\frac{8}{16}$$
$$\frac{9}{16}$$
Correct answer: $$\frac{12}{16}$$
$$\frac{12}{16}$$
$$\frac{1}{2}$$
Correct answer: $$\frac{3}{4}$$
$$\frac{3}{4}$$
Q3.Each face on an 8-sided die has a unique integer from 1 to 8 written on it.
The Venn diagram shows Event A = {factors of 15} and Event B = {even numbers}.
Which of these statements are correct?
Each face on an 8-sided die has a unique integer from 1 to 8 written on it.
The Venn diagram shows Event A = {factors of 15} and Event B = {even numbers}.
Which of these statements are correct?
Events A and B are exhaustive.
Correct answer: Events A and B are not exhaustive.
Events A and B are not exhaustive.
Correct answer: The outcome 7 isn’t in either event A or event B.
The outcome 7 isn’t in either event A or event B.
Correct answer: Events A and B are mutually exclusive.
Events A and B are mutually exclusive.
Events A and B are not mutually exclusive.
Q4.Sam plays a video game that can either be won or lost.
The probability that Sam wins the video game is 61%.
The probability that Sam loses the video game is %
Sam plays a video game that can either be won or lost.
The probability that Sam wins the video game is 61%.
The probability that Sam loses the video game is %
Correct Answer: 39
39
Q5.This table shows the mutually exclusive and exhaustive set of outcomes, and the probability of each outcome, from spinning a spinner once.
Find the value of $$x$$.
This table shows the mutually exclusive and exhaustive set of outcomes, and the probability of each outcome, from spinning a spinner once.
Find the value of $$x$$.
$$\frac{3}{30}$$
$$\frac{7}{30}$$
Correct answer: $$\frac{8}{30}$$
$$\frac{8}{30}$$
$$\frac{11}{30}$$
$$\frac{22}{30}$$
Q6.This table shows the set of outcomes and the probability of each outcome, from spinning a spinner once.
The spinner is spun 1000 times. How many times should you expect the spinner to land on C?
This table shows the set of outcomes and the probability of each outcome, from spinning a spinner once.
The spinner is spun 1000 times. How many times should you expect the spinner to land on C?
Correct Answer: 250
250
Assessment exit quiz
6 Questions
Q1.Lucas spins a spinner with colours: {green, orange, brown}.
P(green) = 30%.
P(orange) = P(brown).
P(brown) = %.
Lucas spins a spinner with colours: {green, orange, brown}.
P(green) = 30%.
P(orange) = P(brown).
P(brown) = %.
Correct Answer: 35
35
Q2.Izzy plays a game she can either win (W), lose (L), or draw (D)
P(W) = 0.55.
P(L) is twice as likely as P(D). P(D) = .
Izzy plays a game she can either win (W), lose (L), or draw (D)
P(W) = 0.55.
P(L) is twice as likely as P(D). P(D) = .
Correct Answer: 0.15, 15%
0.15, 15%
Q3.A game can either be won by Alex, Sam, or Jacob.
By constructing and solving an algebraic equation, find P(Sam wins).
A game can either be won by Alex, Sam, or Jacob.
By constructing and solving an algebraic equation, find P(Sam wins).
0.14
0.2
Correct answer: 0.28
0.28
0.3
0.7
Q4.A spinner with outcomes {A, B, C, D} is spun once.
P(A) = 0.12.
P(B) = $$x$$.
P(C) is twice as likely as P(B).
P(D) is equally likely as P(A or C).
Find an expression for P(D) in terms of $$x$$.
A spinner with outcomes {A, B, C, D} is spun once.
P(A) = 0.12.
P(B) = $$x$$.
P(C) is twice as likely as P(B).
P(D) is equally likely as P(A or C).
Find an expression for P(D) in terms of $$x$$.
$$0.12 + x$$
Correct answer: $$0.12 + 2x$$
$$0.12 + 2x$$
$$0.12 - 2x$$
$$0.12 - x$$
$$0.12 \times x$$
Q5.A bag of marbles only contains white (W), green (G), and cyan (C) marbles.
36% of the marbles are white.
P(G) : P(C) = 3 : 5.
P(C) = %.
A bag of marbles only contains white (W), green (G), and cyan (C) marbles.
36% of the marbles are white.
P(G) : P(C) = 3 : 5.
P(C) = %.
Correct Answer: 40
40
Q6.A bag of sweets only contains four flavours. The table shows the frequency of each type of sweet in the bag.
P(cherry) = $$3\over10$$.
The number of apple sweets in the bag is .
A bag of sweets only contains four flavours. The table shows the frequency of each type of sweet in the bag.
P(cherry) = $$3\over10$$.
The number of apple sweets in the bag is .
Correct Answer: 17
17
