9 Probability of Combined Events

Notes

9.1 Probability of an Event - SPM Mathematics9.1 Probability of an Event The probability of an event A, P(A) is given by P ( A ) = Number of times event A occurs Number of trials P ( A ) = n ( A ) n ( S ) where 0 ≤ P ( A ) ≤ 1 If P(A) = ... Read more

9.2 Probability of the Complement of an Event - SPM Mathematics9.2 Probability of the Complement of an Event 1. The complement of an event A is the set of all the outcomes in the sample space that are not included in the outcomes of event A. 2. The probability of the complement of event A is: P ( A ' ) = 1 − P ... Read more

9.3a Finding the Probability of a Combined Event by Listing the Outcomes - SPM Mathematics9.3 Probability of a Combined Event 9.3a Finding the Probability of a Combined Event by Listing the Outcomes 1. A combined event is an event resulting from the union or intersection of two or more events. 2. The union of combined event ‘A or B’ = A υ B 3. The intersection of combined event ‘A and B’ = A ∩ ... Read more

9.3b Finding the Probability of Combined Events (a) A or B (b) A and B - SPM Mathematics9.3 Probability of a Combined Event 9.3b Finding the Probability of Combined Events (a) A or B (b) A and B 1. The probability of a combined event ‘A or B’ is given by the formula below. P(A or B)=P(A∪B) = n(A∪B) n(S) 2. The probability of a combined event ‘A and B’ is given ... Read more

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Exercises

9.4.1 Probability of Combined Events, SPM Paper (Short Questions) - SPM MathematicsQuestion 1: A bag contains 36 marbles which are black and white. It is given that the probability for a black marble being picked at random from the bag is 5 9 . Calculate the number of white marbles to be taken out from the bag so that the probability of picking a black marble ... Read more

9.4.2 Probability of Combined Events, SPM Paper (Short Questions) - SPM MathematicsQuestion 5:In an office, 300 workers go to work by bus, 60 workers go by car and the rest go by motorcycle. A worker is chosen at random. The probability of choosing a worker who goes to work by bus is ⅔.Find the probability of choosing a worker who does not go to work by ... Read more

9.5.1 Probability of Combined Events, SPM Paper (Long Questions) - SPM MathematicsQuestion 1: All the cards written with the letters from the word ‘INTERNATIONAL’ are put into a box. Two cards are drawn at random from the box, one after another, without replacement. Calculate the probability that (a) the first card drawn has a letter N and the second card drawn has a letter I. (b) ... Read more

9.5.2 Probability of Combined Events, SPM Paper (Long Questions) - SPM Mathematics9.5.2 Probability (II), SPM Practice (Long Questions) Question 3: Diagram below shows two cards labelled with letters in box A and three numbered cards in box B. A card is picked at random from box A and then a card is picked at random from box B. By listing the sample of all possible outcomes ... Read more

9.5.3 Probability of Combined Events, SPM Paper (Long Questions) - SPM MathematicsQuestion 5:A fair dice is tossed. Then a card is picked at random from a box containing a yellow, a red and a purple card.(a) By using the letter Y to represent the yellow card, the letter R to represent the red card and the letter P to represent the purple card, complete the sample ... Read more

9.5.4 Probability of Combined Events, SPM Paper (Long Questions) - SPM MathematicsQuestion 7:Diagram below shows 4 cards labelled with letters.Two cards are chosen at random from the box, one by one, without replacement.(a) List the sample space.(b) Find the probability that(i) at least one card chosen is labelled C,(ii) both cards chosen are labelled with same letter.Solution:(a)Sample space, S= {(C, O1), (C, O2), (C, L), (O1, ... Read more

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