EXPERIMENTAL PROBABILITY
(RELATIVE FREQUENCY)
The Grand National
1.Red Rum
start
finish
2.Monty’s Pass
3.Smartie
4.Best Mate
5.Amberleigh House
6.Rupert
7.Odds On
8.Dan Knee
9.Saint Matthew
10.Big Ben
11.Wilkie’s Gold
12.Son of a Gun
which horse
has the best
chance of
winning and
why?
When you roll two dice and add the scores you can get any
number between 2 and 12, but they are not equally likely
outcomes.
Consider the chances of getting each number.
2
3
4
5
6
7
1+1
1+2
1+3
1+4
1+5
1+6
2+1
3+1
4+1
5+1
2+2
2+3
3+2
8
9
10
11
12
2+6 3+6
4+6
5+6
6+6
6+1
6+2 6+3
6+4
6+5
2+4
2+5
3+5 4+5
5+5
4+2
5+2
5+3 5+4
3+3
3+4
4+4
4+3
There is more chance of getting a 7 than any other
number. So the 7th horse has the greatest probability of
winning. The 2nd and 12th horses have the least chance.
The longer we play the game the more the pattern
should look like an arrow.
start
1.Red Rum
2.Monty’s Pass
3.Smartie
4.Best Mate
5.Amberleigh House
6.Rupert
7.Odds On
8.Dan Knee
9.Saint Matthew
10.Big Ben
11.Wilkie’s Gold
12.Son of a Gun
finish
There are 30 counters in a bag. Tina takes one without
looking. She writes down its colour and then puts the
counter back in the bag. She does this 30 times and
records her results in a chart.
blue
yellow
7
3
green
red
orange
11
4
5
Tina thinks there must be 7 blue
counters in the bag because there
are 7 blues on the chart.
Explain why Tina is wrong.
Tina thinks there can’t be any
white counters in the bag
because there are none on the
chart.
Explain why Tina is wrong.
We can use the table to estimate the probability of 11
Tina picking a green counter next time.
30
Sometimes we can use data from the past to help us
estimate a probability.
Over the last 20 days the school bus has been late 3
times. Estimate the probability that it will be late
tomorrow.
3
20
Yesterday 27 out of 40 year 7 pupils had school dinner.
Estimate the probability of a year 7 pupil chosen at
random from the register having a school dinner today.
27
40
You have an ordinary 6-sided dice and a tetrahedral
dice. Design a sample space diagram that shows all
the possible outcomes when you roll them and add
the scores.
+
1
2
3
4
5
6
1
2
3
4
5
6
7
2
3
4
5
6
7
8
3
4
5
6
7
8
9
4
5
6
7
8
9
10
+
1
2
3
4
5
6
1
2
3
4
5
6
7
2
3
4
5
6
7
8
3
4
5
6
7
8
9
4
5
6
7
8
9
10
Which are the most likely scores?
Which are the least likely scores?
What is the probability of getting a 3 as your next
score?
What is the probability of getting an 8 as your next
score?
If you carried out the experiment 40 times how many
times would you expect to score 8?
score
tally
frequency
2
3
4
5
6
7
8
9
10
Carry out the experiment 40 times. Let’s see if your results
are what you expect.
Did you get 5, 6 or 7 more than any other? Did you
get 8 five times like we predicted?
Use your results to work out the answer to the
following;(remember – you are using your own data to estimate
the probablilities – so your answers may be different from other
people’s)
1. What is the probability of getting a 10 on your next
go?
2. What is the probability of getting a number less than 6
on your next go?
3. What is the probability of getting a 12 on your next
go?
4. What is the probability of getting a multiple of 3 on
your next go?
5. What is the probability of getting a number greater
than 7 on your next go?
The number of times you
would expect to get a 6
when you roll an ordinary
dice 48 times.
The number of times you
would expect to get an odd
number when you roll a
dice 48 times.
The number of times you
would expect to get a
multiple of 3 when you roll
a dice 48 times.
The number of times you
would expect to have to
roll a dice in order to get
a 1 five times.
24
8
16
30
Copy this table in your books
Experiment
number
1
2
3
4
5
6
7
8
9
10
1st
guesses
2nd
3rd
4th
Blue
Yellow
Red
Green
Put four different coloured cubes or counters in an
envelope.
Without looking take a cube or counter from the
envelope but before you do so guess its colour.
If you are right put a tick in the first column of the
table, if you are wrong put a cross.
Put the cube or counter on the table.
Carry on until you have taken out all four cubes or
counters.
Repeat this experiment 10 times and record your
results.
What is the chance of being right on the 1st guess?
What is the chance of being right on the 4th guess?
On which guess are you most likely to be right?
On which guess are you most likely to be wrong?