Question

R=8

100 Question AS BB Café serves macaroni and noodle in the morning. The customers can choose either ham or satay beef as the topping (but not both). The probabilities for a customer to choose macaroni and noodle are 0.4 and 0.6, respectively. If a customer chooses macaroni, the probability of choosing ham as the topping is 0.7 + . If a customer chooses noodle, the probability of choosing ham as the topping is 0.1 Let M, N, H and B be the events that the customer chooses macaroni, noodle, ham and satay beef respectively. (a) Find the probability of the following events. Correct your answers to 3 decimal places (1) A customer chooses noodle with satay beef as topping. (2 marks) (ii) A customer chooses satay beef as the topping. (2 marks) (ii) A customer chooses noodle or satay beef or both. (2 marks) (iv) A customer chooses noodle given that he/she chooses satay beef as the topping. (2 marks) (b) Based on the result in (a(i), explain if event N and event B are mutually exclusive or not. (2 marks)

Answer 1

M: Event that customer chooses macaroni N: Event that customer chooses noodles Event that customer chooses ham topping that customer chooses satay beef topping Enent Ginen, P (M) = 0.4 P(N) = 0.6 1 8 0.78 R "0.7+ (0.7+ 100 P(н) м) P(HIN) = 0.1 P[B]N] 2 P[BON] P[N] (a) (i) Requined probability =P[NnB P[B10] P[N] (- P(HIN)) P[N]. (.. cestomer can choose exactly one of ham or beets, =(1-0.2).0.6 => P (B/N) + P(41/N) = 1 not both 0.540 (correct to 3 decimal places) (it). Required probability P[B [: beef can be chosen chith noodle or with P[(BIN) U (BNM) macaroni = P [BON] + P [BAM] ('. the earts are mutually exclusive) 0.54 P[B]H] P[M] (using part (2)) 0.54 (- PCHIM)) PEM] Coco 0.54 + (1 -0.78) 04 21) + as argued bepre P (BIM) + P(AIM)

-0.628 (coreet upto 3 decimal places) Cult) Required probability = PENUB - P[N] + P [B] - PINOB] (using the formula for union) (by parts (i) & (ii) lus) 0.540 + 0.628 0.688 (conect to 3 decimal places) (6) > Definition: Two enents A and B are said to be mutually exclusine none of the two events can occur simultaneously P[AnB] = 0, From a(i), P Enno -0.540 70 N and B are not mutually exclusive Thus