SUBTOPIC200

32004

2005

2006

Concept of probability P1

Probability of Independent events

P1

Probability of Mutually Exclusive

P1 P1

ANALYSIS OF 2003 – 2006 SPM QUESTIONS

P(A)outcomespossibleallofseta

outcomesdesiredofseta

Sn

An)(

)(

)(1)'(1)(0 APAPandAP

Ex 111 cards containing the letters of the word PROBABILITY is put in a box. A card is taken out at random. Find the probability that the card chosen is

(a) letter B (b) a vowel (c) a consonant

(a)

11)( Sn

2)( Bn

11

2)( BP

(b) 4)( Vn

11

4)( VP

(c) 7)( Cn

11

7)( CP

Ex 2There are x red balls and 8 yellow balls in bag. A ball is taken at random from the bag. The probability of getting a red ball is

.7

3

(a) Find the value of x. (b) If y red balls are then added to the box, the probability of getting a yellow ball becomes ½. Find the value of y.

7

3

8

xx

2437 xx

244 x

6x

Total number of balls = x + 8

Total number of balls = y + 14

2

1

14

8

y

1614 y2y

12

5

7

xx

35512 xx

357 x

5x

SPM‘04

A box contains x orange sweets and 7 strawberry sweets. If a sweet is taken at random from the box, the probability of getting an orange sweet is . Find the value of x.

12

5

12

5)( sweetorangeP

MUTUALLY EXCLUSIVE EVENTS

A B

A B

The probability of event A or event B occurring / not mutually exclusive

The probability of event A and event B mutually exclusive.

)()()()( BAPBPAPBAP

)()()( BPAPBAP 0)( BAPbecause

P(A or B)

P(A or B)

0)( BAP

METHOD

1

2

3

4

5

Find the possible outcomes of each event.

Find the possible outcomes of the sample space.

Find the probability of each event.

Determine if the events are mutually exclusive. Keywords ‘or’ or ‘at least’.

Use the Addition Rule of Probability.

INDEPENDENT EVENTS

Two events are independent if the fact A occurs does not affect the probability of B occurring.

)()()( BPAPBAP

P(A and B)

METHOD

1

2

3

Find the probability of each event.

Determine if the events are dependent.

Use the Multiplication Rule of Probability to calculate of both events.

Ex 4Two dice, one black and the other is white, are tossed together. Find the probability that

(a) an even number appears on the black dice.

(b) the sum of the numbers on the two dice is 7.

(c) an even number appears on the black dice and the sum of the numbers on the two dice is 7.

(d) an even number appears on the black dice or the sum of the numbers on the two dice is 7.

0 1 2 3 4 5 6

1

23

4

5

6

WD

BD

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36)( Sn

)}6,6(),...,2,6(),1,6(),6,4(),...,2,4(),1,4(),6,2(),...,2,2(),1,2{(A(a) A= events of even number appears on the black dice.

2

1

36

18)( AP

(b) B = events with the sum of the numbers on the two dice is 7.

)}1,6(),2,5(),3,4(),4,3(),5,2(),6,1{(B

6

1

36

6)( BP

(c) an even number appears on the black dice and the sum of the numbers on the two dice is 7.

)}1,6(),3,4(),5,2{(BA

12

1

36

3)( BAP

(d) an even number appears on the black dice or the sum of the numbers on the two dice is 7.

0)( BAP

)()()()( BAPBPAPBAP

)( BAP2

16

1

12

1

12

7

Ex 5 Sarah is asked to write a number from the set

{ 1, 2, 3, 3,5 ,6}. Find the probability that she will write

(a) the number 3,

(b) the number 5,

(c) the number 3 or number 5

(a) 3

1

6

2)3( numberP

(b)6

1)5( numberP

(c)6

1

3

1)53( numberornumberP

2

1

BooksPrice index in 2000 based

on 1998

History 5

Geography 6

English 4

SPM‘05

The table shows the number of books on a book shelf. Two books are taken from the shelf at random. Find the probability that both books are of the same category.

),(),(),()( EEPGGPHHPcategorysameP

14

3

15

4

14

5

15

6

14

4

15

5

105

31

SPM‘06

The probability that Hamid qualifies for the final of a track event is while the probability that Mohan qualifies is .

5

2

3

1

Find the probability that

(a) both of them qualify for the final.

(b) only one of them qualifies for the final.

5

3)'(

5

2)(

HP

HPHAMID

3

1

5

2)( MHP

15

2

3

1

5

3

3

2

5

2)'()'( MHPMHP

15

7

3

2)'(

3

1)(

MP

MP

3

2)'(

3

1)(

HP

MPMOHAN