PROBABILITY

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

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)

Ex 2 (a) Find the value of x. ,[object Object],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 .

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.

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)

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. 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 4 Two dice, one black and the other is white, are tossed together. Find the probability that ,[object Object],(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

[object Object],(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.

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

Ex 5 ,[object Object],[object Object],[object Object],[object Object],[object Object],(b) (c)

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

SPM ‘ 06 Find the probability that ,[object Object],(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

PROBABILITY

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