In my case R=1

Question 1 (25 marks) (a) Let A and B be two events. Given the following probabilities for these events: P(A)=0.75, P(B|A)=0.6 and P(BnA) =0.1. (i) What is the probability of P(Bn A) ? (ii) What is the probability of P(B)? (iii) What is the probability of P(A UB) ? (iv) What is the probability of P(A B)? (v) What is the probability of P(A B)? (10 marks) (b) Let x,, X, and x, be a positive integer. + X 2 + X'3 = Consider a system of linear equations 2x, - 5x3 = Using Gauss-Jordan elimination and performing elementary row operations to solve the above system of linear equations and determine ALL the possible combinations of x,, x, and x, . (7 marks) (c) Consider the system of linear equations Wi + tw2 + W3 = 1, where t and m are real twi + 4w2 + 2W3 = m-R, constant. (i) suppose ? : } me][8 42 2 la] Use elementary row operations to determine a and B in terms of t and m. (2 marks) (ii) Hence, find all the value(s) of t and m, if any, such that the given system of linear equations has 1) unique solution 2) no solution 3) infinitely many solutions. (6 marks) Page 2 of 6