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Compare experimental and theoretical probabilities

Coins tossing screenshot

Interactive resources

R1: Identify the mystery spinner: a mystery spinner is spun 100 times and the results recorded. Identify the mystery spinner from the results.

R16: Identify the mystery spinner version 2
Identify the mystery spinner from the results. The spinner can be spun 10, 100, 1000 or 10000 times. Click on the question mark to show the spinner. Stop/start the spinner.

R2: Coins tossing simulation: Toss up to four coins up to 100 times.

 

 

Example of spinner simulation

R3: Spinner simulation (see picture): points are plotted to show the relative frequency of each score against the number of trials. First use the slider to determine the number of trials then play the simulation. The simulation can be started and stopped.

R4: One coin tossing simulation: one coin is tossed and points are plotted to show the relative frequency of heads against the number of trials. First use the slider to determine the number of trials then play the simulation. The simulation can be started and stopped.

To speed up the simulations press the space bar.

The results are updated.
R14: Ten polygons in a house

A rectangle comes out of the houseThere are 10 polygons in a house. At random one polygon will come out of the house and then go back in.
First select how many times you want this to happen: 10, 100, 500 or 1000.
Click 'ok, then the 'play' button.
Click 'stop' to stop the action.
When the number of trials selected have been completed the polygons will all come out of the house if the 'reveal' button is clicked.

Example of the bee simulation
The number of times the bee lands on a flower is recorded.

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A bee collects pollen: probability simulation

The bee moves north, south, east or west.A bee starts in the centre of the grid (see picture) and moves along the lines of a grid of flowers. The bee moves from one flower to the next - up to 5 moves. It will then land on a flower.
At each flower the bee moves north, south, east or west. It is equally likely to move in any of the four directions.
What is the probability it will land on any particular flower?
The first bee simulation will generate random results. First decide how many moves the bee will make and how many trials to run. The simulaltions can be run at two speeds: slow or fast, click on the slow/fast button.
The second bee simulation will generate the expected results.

R5: Bee simulation 1 (random results)

R6: Bee simulation 2 (expected results)

Simulation 1 could be used to introduce the activity. The pupils could then have a go at working out the probabilities on paper.

An example of a  tree diagram

Two dice tree diagram


Dice.. same but different

Tree Diagrams
Coins
Toss either 2, 3 or 4 coins up to 500 times. Watch the tree diagram and bar chart display the outcomes.
First select how many coins you want and the number of trials then click the 'play' button.
Use the buttons below to start and stop the simulation.
The control buttons

R7: Coins tree diagram

Two Dice
Roll two dice up to 500 times, add together the scores. The speed can be either slow or fast: click on the slow/fast button.
Use these buttons to control the simulation

R8: Two dice tree diagram
R9: Two dice expected results
: the dice are rolled 36 times giving the expected results.

R10: Dice... same but different
If two dice are rolled there is one way to score 2, two ways to score 3....one way to score 12.
Find another pair of non-standard dice that give the same number of ways of obtaining the same sums.
There must be at least one dot on each face.

Use these buttons to change the numbers on the diceUse this simulation to choose the number of dots on each face of the dice. The simulation will play all the possible outcomes.
To choose the numbers on the dice: click on the face of a blue or red dice then click on a number button.
Change the speed of the simulation by clicking the slow/ fast button.

Use the Random Birthday Generator

R15: Birthday problem
What is the probability that in a class of 23 at least two people have the same birthday?
Answer: It's more than 50%

This resource will generate random birthdays and stop when two are the same.

Choose a door

GoatR17: The Monty Hall Problem
The Monty Hall problem is a probability puzzle based on an American television game show. The host of the show was Monty Hall.
Contestants were faced with choosing to open one of three doors. Behind one of the doors was a car, behind each of the other two was a goat.
The contestant chose a door and then Monty Hall who knew what was behind each door, opened one of the other two doors to reveal a goat. The contestant then had to decide whether to stick with his or her first choice or switch to the other closed door.
Is it better to switch or stick? Or doesn't it matter? What are the chances of winning the car? The problem provoked a great deal of argument and discussion.

The simulation can be used in two ways. Choose a door yourself and then decide whether to stick or switch or let the computer do the work for you. Decide whether to stick or switch and how many trials.

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Find and justify theoretical probabilities

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Match the spinner with the table
Use Spinners Game

R11: Match the spinner with the frequency table. Eight spinners are spun 100 times and the results recorded in tables. Which spinner goes with which table? Click underneath the spinners to reveal the answers.

R12: Match the spinner with the graph. Eight spinners are spun 100 times and graphs are generated. Which spinner goes with which graph?

 

 

R13: Spinners game
A game is played by spinning each spinner once. To win a prize the two spinners must stop at the same letter. Work out the probability both spinners wil stop at the same letter and how much is won or lost in a game. Click underneath the spinners to reveal the answer.

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