QUESTION 4 Suppose that each time an online shopper buys a a bar of soap, he chooses either brand A or brand B. For each purchase after the rst, the probability is 1/3 that he will choose the same brand that he chose on his preceding purchase and the probability is 2/3 that he will switch brands. If he is equally likely to choose either brand A or brand B on his first purchase, what is the probability that both his rst and second purchases will be brand A and both his third and fourth purchases will be brand B? R 1/2 1/27 3/8 11/27 QUESTION 5 Suppose that SpaceX has just designed a new rocket whose control system has a probability of 0.001 of malfunctioning. Knowing this, the engineers at SpaceX have also placed a duplicate (also malfunctions with a 0.001 probability) and completely independent control system that will take control in case the first system fails. What is the probability that the rocket will be operating under the control ofthe original system or the duplicate system on a given flight? 0.00001 K 0.000001 0.99999 0.999999 1 points 1 points Save Answer Save