Nuffield Free-Standing Mathematics Activity Probability

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© Nuffield Foundation 2011 Nuffield Free-Standing Mathematics Activity Probability

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Nuffield Free-Standing Mathematics Activity Probability. Probability. What is the probability that the bus does not come on time?. What is the probability of all the coins landing heads up?’. - PowerPoint PPT Presentation

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Page 1: Nuffield Free-Standing Mathematics Activity Probability

© Nuffield Foundation 2011

Nuffield Free-Standing Mathematics Activity

Probability

Page 2: 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.

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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

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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

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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?

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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?

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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

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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.