(a) Table 1 represents probabilities for the number of times that a certain computer system will crash in a week. Let A be the event there are more than three crashes during the week. and let B be the event that the system crashes at most two times. Number of crashes Probability 0 0.60 1 0.30 2 0.05 3 0.04 4 0.01 Table 1 Find P(A U3). (3 marks) (b) Draw a tree diagram to count the number of bit strings of length four that starts with 1's or ends with 0's. (4 marks) (c) A system contains two components. A and B. Both components must function for the system to work. The probability that component A fails is 0.08. and the probability that component B fails is 0.05. Assume the two components function independently. nd the probability that the system functions. (3 marks) (d) There are .1' apples in a crate. 3 of the apples are bad. Fathina chooses two apples from . . . . l the crate. w1tliout replacement. The probabihty that she selects two bad apples is . 12 Figure 1 shows probability tree diagram. \\u AJthLll-J) (d) There are x apples in a crate. 3 of the apples are bad. Fathiua chooses two apples from 1 the crate. without replacement. The probability that she selects two bad apples is . Figure 1 shows probability tree diagram. lsT Apple 2nd Apple bod Figure 1: Tree diagram (i) Using tree diagram. show that x2 .\\' 72 = 0 . (ii) Find the number of apples. x in crate. (iii) Find the probability that both apples are good. 12 (4 marks)