Cambridge International Mathematics

2 A pocket in a golf bag contains 6 white and 4 yellow golf balls. Two of them are selected at random

without replacement.

a Determine the probability that:

i both are white ii the first is white and the second is yellow

iii one of each colour is selected.

b Why do your answers inanot add up to 1?

3 A container has 4 purple, 3 blue and 1 gold ticket. Three tickets are selected without replacement. Find

the probability that:

a all are purple b all are blue c the first two are purple and the third is gold.

Tree diagrams can be used to illustrate sample spaces, provided that the alternatives are not too numerous.

Once the sample space is illustrated, the tree diagram can be used for determining probabilities.

ConsiderExample 11again. The tree diagram for this information is:

Smeans Sunil hits

Mmeans Monika hits

Notice that:

² The probabilities for hitting and missing are marked on the branches.

² There arefouralternative paths and each path shows a particular outcome.

² All outcomes are represented and the probabilities of each of the outcomes are obtained bymultiplying

the probabilities along that path.

Example 13 Self Tutor

Stephano is having problems. His desktop computer will only boot up90%of the time and his laptop

will only boot up70%of the time.

a Draw a tree diagram to illustrate this situation.

b Use the tree diagram to determine the chance that:

i both will boot up ii Stephano has no choice but to use his desktop computer.

a D=desktop computer boots up

L=laptop boots up

H USING TREE DIAGRAMS [10.5]

Sunil’s

results

Monika’s

results

S

MSand M

SM'and

S'andM

S'andM'

M'

M

S'

outcome probability

total 1

Rt_

Rt_

Rt_

Qt_

Ty_ Ty_

Ty_

Qy_

Qy_

Ty_

£

£

£

£

=

=

=

=

Qy_ Fe_p_

Qt_ Qy_

Qt_

Ae_p_

Ge_p_

We_Pp_

M'

desktop

laptop

D

LDLand

DLand '

DL' and

DL' and '

L'

L

D'

L'

outcome probability

total 1.00

£

£

£

£

=

=

=

=

0.9

0.9 0.7 0.63

0.9 0.3 0.27

0.1 0.7 0.07

0.1 0.3 0.03

0.7

0.7

0.3

0.3

0.1

522 Probability (Chapter 25)

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Y:\HAESE\IGCSE01\IG01_25\522IGCSE01_25.CDR Monday, 27 October 2008 2:31:23 PM PETER