© Nuffield Foundation 2011
Nuffield Free-Standing Mathematics Activity
Probability
Probability
What is the probability of all the coins landing heads up?’
Sometimes you can work out probabilities, but sometimes you need to use an experiment or past experience.
What is the probability that the bus does not come on time?
In this activity you will use both methods.
Experimental probability
trialsof number Totalhappened E timesof NumberEof frequency Relative
• the probability that a drawing pin lands point up if you drop it onto the floor?
How can you estimate:
• the probability of having an accident at home?
If drawing pin lands point up in 140 out of 200 throws
200140up) P(point = 0.7 10
7
The more data you have, the better the estimate.
• the probability of a train being late?
Think about ... In what other situations can data help you to estimate probabilities?
Probability
iespossibilitof number Totalhappen can E waysof NumberP(E)Theoretical probability
0 1
Probability line
P(more than 2)
32
P(less than 7)P(even)
21
61
P(6)P(7)
If a fair dice is thrown
61P(6)
63P(even)
64P(more than
2)
P(7)
P(less than 7) 21
32
= 0
= 1
must be equally likely
(impossible) (certain)
Think about ...How do these use the fact that the dice is fair?
P(E doesn’t happen)
Expectation
Expected number of trials in which E occurs
= P(E) total number of trials
P(E) = 1 – P(E)
107up) point lands pin P(drawing
103down) point lands pin P(drawing
In 300 throws of a fair dice
expected number of sixes
expected number of even scores
expected number of scores above 2
30061 = 50
30021 = 150
30032 = 200
Think about... What is the probability that the drawing pin lands point down?
List possibilities Use a table
Use a tree diagram
HH, HT, TH, TTHH HTTH TT
H THT
2nd coin
1st coin
1st coin
H
TH
T2nd coin
H
T
HH
HTTH
TT
HH
TH TT
Probabilities if coins are fair
41P(two Hs)
42P(H&T in any order)
P(at least one T)
21
43
Possible outcomes – tossing two coins
Reflect on your workExplain how relative frequency is used to estimate probabilities.Give some examples.
Write down a formula for the theoretical probability of an event E.
Why is it important to assume that dice and coins are fair when you are calculating theoretical probabilities?
Describe three ways of finding probabilities of combined events.
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