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c) d) In a batch of 100 bearings, 10 are detective. If 5 are chosen at random (without replacement), calculate the probability that all 5 are good. (3 marks) An amplifier consists of two independent stages, A and B connected in series as in Figure 1. The output of A is the input to B. The amplifier works if both stages A and B work. If the probability of A working is 0.72 and the probability of the amplifier working is 0.61, calculate the probability that stage B works, given that stage A works. B Figure 1 (2 marks) An electric circuit has two switches A and B connected in parallel as shown in Figure 2. The probability of switches A working is 0.6 and of switch B working is 0.7. Determine the probability that there is a connection between X and Y. e) хо f) B Figure 2 (3 marks) A robot-operated assembly line is developed to produce a range of new products, which are colour-coded black, white, red and green. The assembly line is programmed to produce 11.76% black. 29.41% white. 7.06% red and 51.76% green items. A sample of 180 items were taken and the following distribution was observed. Colour Frequency Black 26 White 43 Red 15 Green 96 Evaluate whether there is evidence that the assembly line needs adjustment at 5% level of significance using chi-square test. (7 marks) |