There are 366 different Starters of The Day, many to choose from. You will find in the left column below some starters on the topic of Probability. In the right column below are links to related online activities, videos and teacher resources.

A lesson starter does not have to be on the same topic as the main part of the lesson or the topic of the previous lesson. It is often very useful to revise or explore other concepts by using a starter based on a totally different area of Mathematics.

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### Probability Starters:

Bus Stop: How many different ways can four people stand in line?

Coloured Sheep: What is the probability of picking a red sheep from the sheep in the field?

Ice Cream: How many different ice cream cones can be made by choosing two scoops from six flavours?

Pick From The Pot: The pot contains 10 counters which are being randomly removed and replaced. How many of each colour do you think are in the pot?

Tran's Hats: In how many different ways might Tran decide to wear his hats in one week?

Bertrand's Box Paradox: Bertrand's box paradox is a paradox of elementary probability theory, first posed by Joseph Bertrand in 1889

Best Dice: Which of the unusual dice would you choose to give you the best chance of winning the prize?

Biased Coin: Use a biased coin to obtain a fair result

How Many Left Handers?: Work out the number of members if the probability of left-handed members being randomly selected is given.

Other Child's Gender: What is the probability that the other child is also a boy?

Perennial Rivals: Which football team will be first to win four games?

Tri-Junction: A real life situation that can be analysed with the use of a tree diagram.

Unfinished Game: Share the prize in a fair ratio according to the probability of each player willing.

#### Tree Diagrams

Calculate the probability of independent and dependent combined events using tree diagrams.

Transum.org/go/?to=treediagrams

### Curriculum for Probability:

#### Years 7 to 9

Pupils should be taught to record, describe and analyse the frequency of outcomes of simple probability experiments involving randomness, fairness, equally and unequally likely outcomes, using appropriate language and the 0-1 probability scale more...

Pupils should be taught to understand that the probabilities of all possible outcomes sum to 1 more...

Pupils should be taught to generate theoretical sample spaces for single and combined events with equally likely, mutually exclusive outcomes and use these to calculate theoretical probabilities more...

#### Years 10 and 11

Pupils should be taught to apply the property that the probabilities of an exhaustive set of mutually exclusive events sum to 1 more...

Pupils should be taught to use a probability model to predict the outcomes of future experiments; understand that empirical unbiased samples tend towards theoretical probability distributions, with increasing sample size more...

Pupils should be taught to calculate the probability of independent and dependent combined events, including using tree diagrams and other representations, and know the underlying assumptions more...

Pupils should be taught to {calculate and interpret conditional probabilities through representation using expected frequencies with two-way tables, tree diagrams and Venn diagrams} more...

#### Years 12 and 13

Pupils should be taught to understand and use mutually exclusive and independent events when calculating probabilities. Link to discrete and continuous distributions more...

Pupils should be taught to understand and use simple, discrete probability distributions (calculation of mean and variance of discrete random variables is excluded), including the binomial distribution, as a model; calculate probabilities using the binomial distribution more...

Pupils should be taught to understand and use conditional probability, including the use of tree diagrams, Venn diagrams, two-way tables. Understand and use the conditional probability formula P(A|B)=P(A∩B)/P(B) more...

Pupils should be taught to understand and use the Normal distribution as a model; find probabilities using the Normal distribution. Link to histograms, mean, standard deviation, points of inflection and the binomial distribution more...

Pupils should be taught to conduct a statistical hypothesis test for the proportion in the binomial distribution and interpret the results in context. Understand that a sample is being used to make an inference about the population and appreciate that the significance level is the probability of incorrectly rejecting the null hypothesis more...

Pupils should be taught to modelling with probability, including critiquing assumptions made and the likely effect of more realistic assumptions more...

Pupils should be taught to select an appropriate probability distribution for a context, with appropriate reasoning, including recognising when the binomial or Normal model may not be appropriate more...

Pupils should be taught to conduct a statistical hypothesis test for the mean of a Normal distribution with known, given or assumed variance and interpret the results in context more...

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### Notes:

Probability is a measure of the weight of evidence, and is arrived at through reasoning and inference. In simple terms it is a measure or estimation of likelihood of the occurrence of an event. The word probability comes from the Latin word probabilitas which is a measure of the authority of a witness in a legal case. Some of the earlier mathematical studies of probability were motivated by the desire to be more profitable when gambling. Today however the practical uses of probability theory go far beyond gambling and are used in many aspects of modern life.

We believe that even adults can, in many cases, have a poor intuition regarding the effects of probability. These activities are designed to help pupils calculate but also get a 'feel' for the principles of probability.

### Probability Teacher Resources:

Dice and Spinners: Computer generated random numbers for games and probability experiments

Dice Bingo: Choose your own numbers for your bingo card. The caller uses two dice and adds the numbers together.

Greater Than: The teacher has a set of six cards numbered 1 to 6. They are placed face down on the teachers desk so that the teacher can pick up one at random which students then have to fit onto a grid.

Likelihood: Arrange some statements in order according to the probability of them happening. Compare your opinion with thousands of others.

Normal Distribution Calculator: A customised online calculator for quickly finding areas under the normal distribution curve.

Plinko Probability: A simulation of a Quincunx (Galton Board) which can be used to create the bell shaped curve of the normal distribution.

Probability Words: A visual aid to highlight the vocabulary of probability and to debate the relationship between the given words.

Significance: A slide presentation showing how to use the chi-squared test to measure significance.

Skunk: A game for the whole Maths class to play involving chance and choice.

Snail Race Projectable: Twelve snails have a race based on the sum of two dice. This is the teachers' version of the race simulation.

t-Test Revision: A slide presentation designed to revise the key aspects of Student's t-Test.

Two Dice Possibility Space: An interactive visual aid showing the possibility space obtained when throwing two dice

### Probability Activities:

Frequency Trees: Use a frequency tree to show two or more events and the number of times they occurred.

Great Expectation: An interactive online activity requiring logical thinking and a certain amount of luck to place the digits on the correct side of the inequality sign.

Hi-Low Predictions: A version of the Play Your Cards Right TV show. Calculate the probabilities of cards being higher or lower.

Likelihood: Arrange some statements in order according to the probability of them happening. Compare your opinion with thousands of others.

Pascal's Triangle: Get to know this famous number pattern with some revealing learning activities

Pin Drop: Estimate the probability of a drawing pin landing point up from experimental data.

Probability: Basic probability questions in an online exercise.

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.

Probability Washing Line: Hang out the washing on the line so that the probability words on the t-shirts are in order.

Remainder Race: A game involving chance and choice requiring an ability to calculate the remainder when a two digit number is divided by a single digit number.

Snail Race: A race between 12 snails. Which snail is most likely to win? This is the students' version of the race simulation.

Superior: A game for two players who compete to make the largest possible number from randomly selected cards.

The Maths of Gambling: Gambling is never a good idea and this activity might help you understand the mathematics involved.

Tree Diagrams: Calculate the probability of independent and dependent combined events using tree diagrams.

Finally there is Topic Test, a set of 10 randomly chosen, multiple choice questions suggested by people from around the world.

Alternatively, for the more advanced student, there is an ever-growing collection of Exam-Style Questions with worked solutions on the topic of Probability.

### Probability Investigations:

Beginning with One: Is it true that most numbers begin with the digit one? Think of numbers you see everyday and it is a surprising fact that so many of them begin with a one. Can you think why this is true?

Dice Investigation: Throw two dice and multiply the scores. Investigate the different products you can obtain. What about adding? What about using three dice?

Egg Box Investigation: In how many different ways can two eggs be arranged in an egg box?

House Painting: The houses in Mathsland are all three storeys tall. Each storey is painted using one colour. How many ways can the houses be painted?

Predictive Survey: An eight question survey collecting data for an amazing probability experiment.

Traffic Jams: How many ways can three cars be lined up in a traffic jam?

### Probability Videos:

Transum's Probability Video

Calculator Dice Video: If you have no dice don't despair because most scientific calculators have a random number generating facility as can be seen in this short video.

GCSE Probability Part 1: Screencast of probability lesson for Intermediate GCSE Maths.

Probability Video: A reminder of how to work out basic probability leading to simple combined events and expected values.

Statistical Significance: This video explains numeric and categorical data and helps you gain an understanding of when to apply a t-test or a chi-square test.

Tree Diagrams Video: Tree diagrams can be really helpful showing combinations of two or more events in order to calculate probabilities.

### Probability Worksheets/Printables:

Pascal's Triangle Worksheet: Various forms of Pascal's Triangle ready for printing.

Snail Race Board: If pupils are unable to play the Snail Race online this printable board can be used with counters and dice.

Links to other websites containing resources for Probability are provided for those logged into 'Transum Mathematics'. Subscribing also opens up the opportunity for you to add your own links to this panel. You can sign up using one of the buttons below:

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### Other

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#### Frequency Trees

Use a frequency tree to show two or more events and the number of times they occurred.

Transum.org/go/?to=ftree

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M. F. Kuali, Mount Fletcher

Thursday, March 29, 2012

"I like this topic because it helps one to predict the the future outcomes of most of the events happening in the world , e . g . weather focus."

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