Checking and securing calculating probabilities from tables | Maths

Starter quiz

Here are three decks of cards. A single card from each of Deck 1, Deck 2, and Deck 3 is drawn to make a trio. What is the probability that this trio of cards contains a square number?

$\frac{1}{6}$

$\frac{3}{7}$

$\frac{5}{8}$

$\frac{2}{3}$

$\frac{5}{6}$ ✓
Sam plays a video game that can either be won or lost. The probability that Sam wins the video game is 0.42. The probability that Sam loses the video game is ______.

'0.58' ✓
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 ______.

'0.33' ✓
Which of these statements are correct for this frequency tree?

$x$ is equal to $y$

$y$ = 400 ✓

$y$ = 600

$z$ = 150

$z$ = 250 ✓
Each card on a deck of 7 cards has a unique integer written on it. A = {factors of 6}, B = {numbers ≥ 6}. What positive integer could be on the seventh card for events A and B to not be exhaustive?

0

4 ✓

5 ✓

7

12
A game can either be won by either Alex, Sam, or Jacob. P(Sam wins) = ______.

'0.4' ✓

Exit quiz

Students were asked whether they walked to school or used other transport methods, and how long their journey took them. Find the probability a student had a journey of over 15 minutes.

$\frac {3}{10}$

$\frac {2}{3}$

$\frac {7}{10}$ ✓

$\frac {3}{4}$
A spinner with outcomes {1, 2, 3, 5, 9, 15} is spun twice. The outcome of each spin is added together. Find P(multiple of 10).

$\frac{3}{36}$

$\frac{6}{36}$ ✓

$\frac{1}{12}$

$\frac{1}{6}$ ✓

$\frac{1}{2}$
A spinner with outcomes {1, 2, 3, 5, 9, 15} is spun twice. The outcome of each spin is added together. Find P(not a prime number).

$\frac{24}{36}$

$\frac{25}{36}$ ✓

$\frac{5}{6}$

$\frac{2}{3}$
People at a bus station were surveyed their age and where their destination was. Match each frequency from the table to its value.

$a$

⇔

181 ✓

$b$

⇔

144 ✓

$c$

⇔

70 ✓

$d$

⇔

20 ✓

$e$

⇔

270 ✓

$f$

⇔

230 ✓
People at a bus station were surveyed their age and where their destination was. A person is chosen at random. Find P(60 or over and going to Rowanwood).

$\frac{29}{173}$

$\frac{29}{500}$ ✓

$\frac{173}{500}$

$\frac{144}{500}$

$\frac{144}{173}$
People at a bus station were surveyed their age and where their destination was. A person going to Oakfield is chosen at random. Find P(under 60).

$\frac{181}{500}$

$\frac{181}{257}$

$\frac{76}{500}$

$\frac{76}{257}$ ✓

$\frac{76}{181}$

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Lesson Details

Key learning points

The probability of an outcome can be found by considering a table
The probability of an event can be found by considering a table showing all possible outcomes
The probability of an outcome can be found by considering a two-way table showing all possible outcomes for two events
The probability of an event can be found by considering a two-way table showing all possible outcomes for two events

Common misconception

Pupils may get confused between two-way tables that show outcomes and two-way tables that show frequencies (particularly when the outcomes are numbers, such as the sum of two dice rolls).

Two-way tables can be either used to display the sample space of individual outcomes or the frequencies of outcomes. Therefore, when using a table, it can be helpful to note down what type of data the table shows.

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.
Frequency - The frequency is the number of times an event occurs; or the number of individuals (people, animals etc.) with some specific property.