2 (Probability)_Soln_2023 (SAJC)

1 ST ANDREW’S JUNIOR COLLEGE JC1 H1 MATHEMATICS (8865) Term 3 Weekend Assignment 2 Topic: Probability Name: ______________________________ Marks:________/10 C.G.: __________ 1 JPJC Promo 8865/2021/Q5 (a) Events A and B are such that ( )P 0.6A = , ( )P 0.4B = and ( )P ' | 0.8BA = . (i) Describe in words what is meant by ( )P ' |BA . [1] (ii) Find ( )P' AB . [1] (iii) Find ( )P AB . [1] (iv) Find ( )P' AB . [2] (b) A box contains 7 red balls and 3 green balls. Two balls are drawn, one after the other, without replacement. (i) Draw a tree diagram to represent the possible outcomes. [2] (ii) Find the probability that one red ball and one green ball are drawn. [2] (iii) Find the probability that the first ball drawn is red given that one red ball and one green ball are drawn. [3]

2 Solutions 1(ai) ( )P ' |BA is the probability that the complement of event B happens given that event A has happened. (aii) ( )P ' | 0.8BA = ( ) ( ) P' 0.8P BA A  = ( ) ( )P ' 0.8 P 0.8 0.6 0.48A B A =  =  = (aiii) ( ) ( ) ( )P P P ' 0.6 0.48 0.12A B A A B = −  = − = (aiv) ( ) ( ) ( ) ( )P ' P +P ' P 'A B A B A B = −  0.6+(1 0.4) 0.48 0.72= − − = (bi) (bii) ( ) 7 1 3 7 7P one red ball and one green ball are drawn 10 3 10 9 15=  +  = (biii) ( )P first ball is red | one red ball and one green ball ( ) ( ) ( ) ( ) P first ball is red one red ball and one g reen ball= P one red ball and one green ball P first ball is red second ball is green P one red ball and one green ball 71 10 3 7 15 1 2  =  = = Red Green 7 10 3 10 Red Green 7 9 2 9 Red Green 62 93= 31 93=