Checking and securing calculating probabilities from diagrams | Maths

Starter 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 15 minutes or under.

$\frac {3}{10}$ ✓

$\frac {1}{3}$

$\frac {2}{3}$

$\frac {7}{10}$
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 5).

$\frac{6}{36}$

$\frac{8}{36}$ ✓

$\frac{10}{36}$

$\frac{1}{9}$

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

$\frac{10}{36}$

$\frac{11}{36}$ ✓

$\frac{12}{36}$

$\frac{13}{36}$
People at a bus station were surveyed their age and where their destination was. Match each frequency from the table to its value.

$a$

⇔

141 ✓

$b$

⇔

84 ✓

$c$

⇔

80 ✓

$d$

⇔

40 ✓

$e$

⇔

190 ✓

$f$

⇔

210 ✓
People at a bus station were surveyed their age and where their destination was. A person is chosen at random. Find P(under 60 and going to Oakfield).

$\frac{141}{500}$

$\frac{141}{207}$

$\frac{66}{207}$

$\frac{66}{400}$ ✓

$\frac{66}{141}$
People at a bus station were surveyed their age and where their destination was. A person going to Rowanwood is chosen at random. Find P(60 or over).

$\frac{84}{400}$

$\frac{84}{113}$

$\frac{29}{84}$

$\frac{29}{113}$ ✓

$\frac{29}{400}$

Exit quiz

A set of events are ______ if at least one of them has to occur whenever the experiment is carried out.

'exhaustive' ✓
A survey asked people whether they lived in Oakfield or not, and if they last shopped by online delivery or by going in-store. A random person is selected. Match each event to its probability.

P(lives in Oakfield)

⇔

$250\over400$ ✓

P(doesn't live in Oakfield)

⇔

$150\over400$ ✓

P(shops in-store)

⇔

$260\over400$ ✓

P(shops online)

⇔

$140\over400$ ✓

P(lives in Oakfield and shops online)

⇔

$100\over400$ ✓
A swimming club has 80 members. There are 13 members who swim both front crawl (FC) and butterfly (BF). The value of $x$ is ______.

'20' ✓
This probability tree shows the probability of one of two events occurring. The value of $x$ is ______.

'0.65' ✓
Lucas and Izzy each play one game of squash that they can either win or lose. P(Lucas wins) = 0.6, P(Izzy wins) = 0.7. Use the probability tree to find the probability that they both lose their game.

0.012

0.12 ✓

0.13

0.42

0.7
Lucas and Izzy each play one game of squash that they can either win or lose. P(Lucas wins) = 0.6, P(Izzy wins) = 0.7. The probability that at least one of them loses their match is ______.

'0.58' ✓

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Lesson Details

Key learning points

The probability of an outcome can be found by considering a tree diagram
The probability of an event can be found by considering a tree diagram
The probability of an outcome can be found by considering a Venn diagram
The probability of an event can be found by considering a Venn diagram

Common misconception

Pupils may add the probabilities along branches of a probability tree, rather than multiplying them.

Remind pupils that probabilities cannot be greater than 1 and demonstrate that adding across the branches sometimes results in a probability that is greater than 1. Therefore, it must be wrong.

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