1. Nuffield Free-Standing Mathematics Activity
Probability

2. Probability
What is the probability of all the coins landing heads up?’
What is the probability that the bus does not come on time?
Sometimes you can work out probabilities, but sometimes you need to use an experiment or past experience.
In this activity you will use both methods.

3. Probability How can you estimate:
• the probability that a drawing pin lands point up if you drop it onto the floor?
• the probability of a train being late?
• the probability of having an accident at home?
Experimental probability
If drawing pin lands point up in 140 out of 200 throws
= 0.7
Think about ... In what other situations can data help you to estimate probabilities?
The more data you have, the better the estimate.

4. Theoretical probability
must be equally likely
If a fair dice is thrown
P(6)
Think about ... How do these use the fact that the dice is fair?
P(7)
= 0
P(even)
P(less than 7)
= 1
P(more than 2)
Probability line
P(6)
P(even)
P(more than 2)
(impossible) 1
(certain)
P(7)
P(less than 7)

5. P(E doesn’t happen)
P(E) = 1 – P(E)
Think about... What is the probability that the drawing pin lands point down?
Expectation
Expected number of trials in which E occurs
= P(E)  total number of trials
In 300 throws of a fair dice
expected number of sixes
= 50
expected number of even scores
= 150
expected number of scores above 2
= 200

6. Possible outcomes – tossing two coins
List possibilities
Use a table HH HT TH TT H T
2nd coin
1st coin
HH, HT, TH, TT HH TH TT
Use a tree diagram
2nd coin H T HH
Probabilities if coins are fair
1st coin H T HT
P(two Hs) H T TH
P(H&T in any order) TT
P(at least one T)

7. Reflect on your work
Explain 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.