Compare
experimental and theoretical probabilities 

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.


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.


R14:
Ten polygons in a house
There
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.

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

A
bee collects pollen: probability simulation
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.


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.
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.
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 nonstandard dice that give the same number of ways
of obtaining the same sums.
There must be at least one dot on each face.
Use
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.


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.


R17:
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.
