RI S1B Probability_tutorial (Solns)

RAFFLES INSTITUTION H2 Mathematics (9758) 2025 Year 6 _____________________ Tutorial S1B: Probability Page 1 of 16 Tutorial S1B: Probability 1 It is given that events A and B are independent and 5P( ) 8AB , 7P( ') 24AB . Calculate (i) P( )B , (ii) P( )A , (iii) P( )AB , (iv) P( ' ')AB . [(i) 1 3 (ii) 7 16 (iii) 7 48 (iv) 41 48 ] Solution AB 'AB 5P( ) 8AB 7P( ') 24AB (i)     P = P P 'BA BA B   from diagram 57= 82 4 1= 3 (ii) Since A and B are independent, A and B’ are independent     P' = P P 'AB A B So    P'P= P' ABA B  7 24= 11 3 7= 16 OR      P= P + P PAB A B AB    PPP P ABA B since A and B are independent events    51 1 P P83 3 7P 16 AA A    (iii) Since A and B are independent events,   P = P PAB A B 71 16 3 7 48 (iv)    P' ' = 1 PA BA B  7 1 48 41 48 A B A B A B

Raffles Institution H2 Mathematics 2025 Year 6 _____________________________________________________________________________________________ ___________________ Tutorial S1B: Probability Page 2 of 16 2 SAJC Prelim 9740/2010/02/Q7a A & B are two events with non-zero probability. Explain if each of the following statements is necessarily true, necessarily false, or neither necessarily true nor necessarily false. (i) If A & B are mutually exclusive, then they are independent. [1] (ii) If A & B are independent, then they are mutually exclusive. [1] Solution (i) If A & B are mutually exclusive, then () 0PA B But since P( ) 0A  and P( ) 0B  , () 0 P ( ) P ( )P AB A B  i.e. A and B are not independent. Statement is necessarily false. OR P( )P( | ) 0 (since and are mutually exclusive)P( ) If and are independent, then P( | ) P( ) 0 contradiction!! ABAB A B B AB A B A   (ii) If A & B are independent, then P( ) P( )P( ) 0AB A B  since P( ) 0, P( ) 0.AB Hence, P( ) 0 . and are not mutually exclusive. AB AB AB      Statement is necessarily false.

Raffles Institution H2 Mathematics 2025 Year 6 _____________________________________________________________________________________________ ___________________ Tutorial S1B: Probability Page 3 of 16 3 DHS JC2 Prelim 9758/2019/02/Q7 In a school survey, a group of 80 students ar e asked about how much time per week (to nearest hour) they spend on their co-curricular activities (CCA). The readings are shown below: CCA (hours) 3 or less 4 to 6 7 or more Boy 17 20 10 Girl 18 15 k k A student is select ed random from the grou