Apologies as Q (V) & (Vi) are at top of page.

An enterprising graduate who has been unable to nd gainful employment has taken to visiting an office block in town each lunchtime with an array of freshly made sandwiches and beverages for sale. Let A be the event that that a customer will purchase a sandwich and say the probability of that event is P(A) = 0.55 . Let B be the event that a customer will purchase a beverage and say the probability ofthat event is PU?) = 0.40 The probability that a customer will purchase both a sandwich and a beverage is, PCA n B) = 0.35 . Provide answers to the following questions correct to 3 decimal places. _ (i)What is the probability that the customer does not buy a sandwich? i.e. Find PCA) . httpszllnuigalwayblackb. (ii) What is the probability that the customer buys a beverage given they buy a sandwich? i.e. Find P(BIA) . (iii) What is the probability that a customer does not buy a sandwich and buys a beverage? i.e. Find Pan 3) (iv) What is the probability that a customer buys a beverage given they did not buy a sandwich? i.e. Find PUNK) (v) Are the two events A and B mutually exclusive? Choose one of the following answers: a) Yes, P(A and B)=0. b) Yes, P(B | A)=P(B) c) No, P(A and B) # 0. d) No, P(B | A) # P(B) e) No, P(A and B)=0. f) No, P(B | A)=P(B) g) Yes, P(A and B) # 0. h) Yes, P(B | A) # P(B) Ans : (Insert one of a/b/c/d/e/f/g/h) (vi) Are the two events A and B independent? Choose one of the following answers: a) Yes, P(A and B)=0. b) Yes, P(B | A)=P(B) c) No, P(A and B) # 0. d) No, P(B | A) #P(B) e) No, P(A and B)=0. f) No, P(B | A)=P(B) g) Yes, P(A and B) # 0. h) Yes, P(B | A) # P(B) Ans : (Insert one of a/b/c/d/e/f/g/h)