The document discusses probability concepts and examples that appeared in SPM exam questions from 2003 to 2006. It covers topics like probability of events, mutually exclusive and independent events, and examples calculating probabilities using different rules. It provides the definition and methods to determine if events are mutually exclusive or independent. It also includes sample probability questions and solutions from past SPM exams.

1. PROBABILITY ANALYSIS OF 2003 – 2006 SPM QUESTIONS P1 P1 2005 P1 2006 P1 2004 Probability of Mutually Exclusive Probability of Independent events Concept of probability 2003 SUBTOPIC

2. PROBABILITY OF AN EVENT P(A)

3. Ex 1 11 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) (b) (c)

4. Ex 2 (a) Find the value of x. If y red balls are then added to the box, the probability of getting a yellow ball becomes ½. Find the value of y. Total number of balls = x + 8 Total number of balls = y + 14 There 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 .

5. 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.

6. MUTUALLY EXCLUSIVE EVENTS The probability of event A or event B occurring / not mutually exclusive The probability of event A and event B mutually exclusive. because P(A or B) P(A or B)

7. 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.

8. INDEPENDENT EVENTS Two events are independent if the fact A occurs does not affect the probability of B occurring. P(A and B)

9. 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.

10. Ex 4 Two dice, one black and the other is white, are tossed together. Find the probability that 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 2 3 4 5 6 WD BD

11. A= events of even number appears on the black dice. (b) B = events with 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.

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

13. 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, the number 5, (c) the number 3 or number 5 (b) (c)

14. 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. 4 English 6 Geography 5 History Price index in 2000 based on 1998 Books

15. SPM ‘ 06 Find the probability that both of them qualify for the final. (b) only one of them qualifies for the final. The probability that Hamid qualifies for the final of a track event is while the probability that Mohan qualifies is . HAMID MOHAN