Checking and securing calculating probabilities from diagrams
I can calculate probabilities from probability trees and Venn diagrams.
- Year 11
Checking and securing calculating probabilities from diagrams
I can calculate probabilities from probability trees and Venn diagrams.
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
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.
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.
Licence
Lesson video
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Prior knowledge starter quiz
6 Questions
Q1.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.
Q2.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).
Q3.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).
Q4.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
Q5.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).
Q6.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).
Assessment exit quiz
6 Questions
Q1.A set of events are if at least one of them has to occur whenever the experiment is carried out.
Q2.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) - $$100\over400$$
Q3.A swimming club has 80 members. There are 13 members who swim both front crawl (FC) and butterfly (BF). The value of $$x$$ is .
Q4.This probability tree shows the probability of one of two events occurring.
The value of $$x$$ is .
Q5.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.
Q6.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 .
