Checking and securing exhaustive events | Maths | Quizalize & Oak National Academy

Starter quiz

Each card in a deck of 10 cards has a unique integer from 1 to 10 written on it. There are ______ factors of 12 in the deck.

'5' ✓
Each card in a deck of 10 cards has a unique integer from 1 to 10 written on it. A single random card is drawn. What is the probability of that card being a factor of 12?

$\frac{4}{10}$

$\frac{5}{10}$ ✓

$\frac{5}{12}$

$\frac{1}{2}$ ✓

$\frac{2}{5}$
Each card in a deck of 10 cards has a unique integer from 1 to 10 written on it. A single random card is drawn. Match each event to its likelihood.

P(greater than 20)

⇔

impossible ✓

P(square)

⇔

unlikely ✓

P(odd)

⇔

even chance ✓

P(single digit)

⇔

likely ✓
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.

'15' ✓
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 a B?

$\frac{5}{15}$

$\frac{3}{15}$ ✓

$\frac{1}{3}$

$\frac{1}{5}$ ✓

$\frac{1}{15}$
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 doesn't contain an odd number?

$\frac{3}{15}$

$\frac{5}{15}$ ✓

$\frac{6}{15}$

$\frac{2}{3}$

$\frac{1}{3}$ ✓

Exit quiz

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 12} and Event B = {even numbers}. Which of these statements are correct?

Events A and B are exhaustive.

Events A and B are not exhaustive. ✓

The outcomes 5 and 7 are not in either event A or event B. ✓

Events A and B are mutually exclusive.

Events A and B are not mutually exclusive. ✓
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 24} and Event B = {odd numbers}. Which of these statements are correct?

Events A and B are exhaustive. ✓

Events A and B are not exhaustive.

The outcomes 1 and 3 are not in either event A or event B.

Events A and B are mutually exclusive.

Events A and B are not mutually exclusive. ✓
Each face on an 8-sided die has a unique integer from 1 to 8 written on it. The Venn diagram shows Event A = {multiples of 4} and Event B = {prime numbers}. Which of these statements are correct?

Events A and B are exhaustive.

Events A and B are not exhaustive. ✓

The outcome 1 isn’t in either event A or event B. ✓

Events A and B are mutually exclusive. ✓

Events A and B are not mutually exclusive.
Sam plays a video game that can either be won or lost. The probability that Sam wins the video game is 56%. The probability that Sam loses the video game is ______%.

'44' ✓
This table shows the mutually exclusive and exhaustive set of outcomes, and the probability of each outcome, from spinning a spinner once. The value of $x$ is ______.

'0.3' ✓
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?

'200' ✓

Worksheet

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Lesson Details

Key learning points

Probabilities can be given as fractions, decimals or percentages
An event is exhaustive if all possible outcomes are included
The probability of an exhaustive event is 1 and this can be used to calculate missing probabilities

Common misconception

Pupils may think that any set of probabilities relating to a scenario will always sum to 1.

Probabilities sum to 1 when the events are exhaustive and mutually exclusive.

Keywords

Mutually exclusive - Two or more events are mutually exclusive if they share no common outcome.
Exhaustive events - A set of events are exhaustive if at least one of them has to occur whenever the experiment is carried out.