Cambridge International Mathematics

Example 15 Self Tutor

A bin contains 4 blue and 5 green marbles. A marble is selected from this bin and its colour is noted.

It is thenreplaced. A second marble is then drawn and its colour is noted. Determine the probability

that:

a both are blue b the first is blue and the second is green

c there is one of each colour.

Tree diagram:

B=blue

G=green

a P(both blue)

=^49 £^49

=^1681

b P(first is B and second is G)

=^49 £^59

=^2081

c P(one of each colour)

=P(B then G or G then B)

=P(B then G)+P(G then B)

=^49 £^59 +^59 £^49

=^4081

Example 16 Self Tutor

Sylke has bad luck with the weather when she takes her summer holidays.

She estimates that it rains60%of the time and it is cold70%of the time.

a Draw a tree diagram to illustrate this situation.

b Use the tree diagram to determine the chance that for Sylke’s holidays:

i it is cold and raining ii it is fine and cold.

a C=the weather is cold R=it is raining

biP(it is cold and raining)

=P(CandR)

=0: 7 £ 0 : 6

=0: 42

ii P(it is fine and cold)

=P(R^0 andC)

=0: 4 £ 0 : 7

=0: 28

1st marble

2nd marble

B

B B and B

B and G

G and B

G and G

G

B

G

G

outcome probability

total 1

£

£

£

£

=

=

=

=

Ro_

Ro_ Ro_ Ro_

Ro_

Ro_

Ro_

To_

To_

To_

To_

To_ To_ To_

Qi_Yq_

Wi_Pq_

Wi_Pq_

Wi_Tq_

temperature rain

C

RCRand

CR'and

C'andR

C'andR'

R'

R

C'

outcome probability

total 1.00

£

£

£

£

=

=

=

=

0.7

0.7 0.6 0.42

0.7 0.4 0.28

0.3 0.6 0.18

0.3 0.4 0.12

0.6

0.6

0.4

0.4

0.3

R'

Probability (Chapter 25) 525

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Y:\HAESE\IGCSE01\IG01_25\525IGCSE01_25.CDR Monday, 27 October 2008 2:31:31 PM PETER