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- 4.5 Equally likely outcomes.
- 4.6 Combined Events.
- 4.11 Conditional probabilities.

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Here are some related resources in alphabetical order. Some may only be appropriate for high-attaining learners while others will be useful for those in need of support. Click anywhere in the grey area to access the resource.

- Pin Drop Estimate the probability of a drawing pin landing point up from experimental data.
- Probability Video A reminder of how to work out basic probability leading to simple combined events and expected values.
- Probability Basic probability questions in an online exercise.
- Venn Diagram Place each of the numbers 1 to 16 on the correct regions on the Venn diagram.
- Snail Race Projectable Twelve snails have a race based on the sum of two dice. This is the teachers' version of the race simulation.
- Snail Race A race between 12 snails. Which snail is most likely to win? This is the students' version of the race simulation.
- Two Dice Possibility Space An interactive visual aid showing the possibility space obtained when throwing two dice
- Venn Totals Practise reading and creating Venn diagrams containing two and three sets and the number of elements in those sets.
- Venn Paint Video Here is a demonstration of how to illustrate union, intersection and complement of sets as they appear in Venn diagrams.
- Tree Diagrams Video Tree diagrams can be really helpful showing combinations of two or more events in order to calculate probabilities.
- Venn Paint Flood fill the regions of the Venn diagrams according to the given statements.
- Tree Diagrams Calculate the probability of independent and dependent combined events using tree diagrams.
- Venn Diagram Pairs The traditional pairs or pelmanism game adapted to test knowledge of Venn diagrams.
- The Maths of Gambling Gambling is never a good idea and this activity might help you understand the mathematics involved.
- Probability Formulae Show that you know which formula (as given in the IB Formula Booklet) to use for each probability question. A drag and drop challenge.

Here are some exam-style questions on this topic:

- "
*If the universal set is the set of positive even numbers less than 30 and:*" ... more - "
*(a) Complete the Venn diagram with the following information.*" ... more - "
*(a) Complete the Venn diagram to represent this information:*" ... more - "
*The following table shows the probabilities of winning certain prizes at a stall in Faulton Towers theme park. A prize is always given for every turn.*" ... more - "
*Derren thinks he is a mind reader and can tell what Paige is thinking. An experiment was conducted to test this.*" ... more - "
*The midnight train to Georgia is not the most reliable. The probability that the train will be late on any day is 0.35*" ... more - "
*At the Trantown annual Fayre there are a number of different sideshows designed to raise money for cancer research. Roger is looking after two of these, the lucky dip and the raffle.*" ... more - "
*The table shows the shoe sizes of 35 male teachers.*" ... more - "
*(a) There are 24 people at a Football Club supporters' meeting in Dudley. Thirteen of them are female.*" ... more - "
*Mrs Gill wants to give her nephew two sweets from a jar she keeps on her kitchen table. There are 11 sweets in this jar.*" ... more - "
*Aran, Betsy and Connor collect data about which way up a drawing pin will land if dropped from a fixed height. Here are their results.*" ... more - "
*During a demonstration for Year 10 pupils a biased coin in a computer simulation landed on heads 600 times.*" ... more - "
*A driving test has two sections, practical(p) and theory(t). One day everyone who took the test passed at least one section. 77% passed the practical section and 81% passed the theory section.*" ... more - "
*The Venn diagram represents a collection of 40 books on sale in an online store.*" ... more - "
*A box contains only green and yellow crayons.*" ... more - "
*Lisa's nephew Sean has two boxes containing plastic building bricks.*" ... more - "
*Twenty nine children went to a zoo to photograph some animals. The numbers of children who photographed Lions(L), Monkeys(M) and Zebras (Z) are given as follows:*" ... more - "
*Neal is attending a Scout jamboree in Japan. He has both boots and trainers to wear. He also has the choice of wearing a cap or not.*" ... more - "
*Donna is in a class of 25 students, 5 of whom have a pet dog.*" ... more - "
*Let \(J\) and \(T\) be independent events, where \(P(J)=0.4\) and \(P(T)=0.7\).*" ... more - "
*On the day after one GCSE paper Twitter and the media were buzzing with comments about a particular question about Hannah's sweets. Here is the Transum version of this now famous Maths exam question:*" ... more - "
*When the arrow is spun once on this spinner, a 1 or a 2 or a 3 can be scored depending on the colour the arrow lands on.*" ... more - "
*Let A and B be events such that \(P (A) = 0.45\) , \(P (B) = 0.35\) and \(P (A \cup B) = 0.5\).*" ... more - "
*Bag A contains 6 green tickets and 5 blue tickets.*" ... more - "
*Sumville has three newspapers: The Chronicle, The Express and Moon, and The Scribe.*" ... more - "
*Piers wins one of the many prizes on offer in the school raffle but he does not yet know exactly what the prize is.*- The probability that a prize is something to eat is 0.3
- The probability that a prize is worth more than $10 is 0.2
- The probability that a prize is something to eat or worth more than $10 is 0.4

*Find the probability that the prize Piers wins is not both something to eat and worth more than $10 as Piers does not like expensive food.*" ... more - "
*The time in minutes taken to drive through a city at different times of the day can be modelled by a normal distribution with mean of 45 and standard deviation of 12. A commuter will be late for work if it takes more than an hour to drive through the city.*" ... more - "
*The Venn diagram below shows the events \(A\) and \(B\), and the probabilities p, q and r.*" ... more - "
*900 professional footballers were surveyed with the following results*" ... more - "
*A game at a fayre consists of a players throwing one dart at the board pictured below.**The probability of hitting each region and the points scored for hitting that region is given in this table.*" ... more - "
*Julie chooses a cake from a yellow box on a shelf. The box contains two chocolate cakes and three plain cakes. She eats the cake and chooses another one from the box. The tree diagram below represents the situation with the four possible outcomes where C stands for chocolate cake and P for plain cake.*" ... more - "
*Jane and David play two games of golf. The probability that Jane wins the first game is \(\frac56\). If Jane wins the first game, the probability that she wins the second game is \(\frac67\).*" ... more - "
*Mathsland's national currency comes in denominations of 1 unit, 5 units, 10 units and 50 units. Sofya places this collection of these coins in her purse then, without looking, takes out two coins at random, one after the other.*" ... more - "
*The weights of players in a sports league are normally distributed with a mean of 75.2 kg, (correct to three significant figures). It is known that 75% of the players have weights between 67 kg and 80 kg. The probability that a player weighs less than 67 kg is 0.05.*" ... more - "
*Eels are elongated fish, ranging in length from 5cm to 4m. In a certain lake the length of the eels are normally distributed with a mean of 84cm and a standard deviation of 18cm. Eels are classified as giant eels if they are more than 120 cm long.*" ... more - "
*Two events A and B are such that \(P(A) = 0.57\) and \(P (A \cap B) = 0.21\).*" ... more

Here are some Advanced Starters on this statement:

**Bertrand's Box Paradox**

Bertrand's box paradox is a paradox of elementary probability theory, first posed by Joseph Bertrand in 1889 more**Best Dice**

Which of the unusual dice would you choose to give you the best chance of winning the prize? more**Biased Coin**

Use a biased coin to obtain a fair result more**How Many Left Handers?**

Work out the number of members if the probability of left-handed members being randomly selected is given. more**Other Child's Gender**

What is the probability that the other child is also a boy? more**Perennial Rivals**

Which football team will be first to win four games? more**Tri-Junction**

A real life situation that can be analysed with the use of a tree diagram. more**Unfinished Game**

Share the prize in a fair ratio according to the probability of each player willing. more

Click on a topic below for suggested lesson Starters, resources and activities from Transum.

This Scheme of Learning was produced by White Rose Maths and is used here with permission granted on 30th June 2021.