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Question 4 (a) If a coin is flipped, the probability of it landing on heads on any flip is 0.4. After 20 coin flips, determine the probability that: () There are exactly 2 heads. (ii) There are exactly 10 heads. (iii) There are between 3 and 7 heads. [12 marks] (b) In a bolt factory there are three machines: A, B and C. Machines A, B and C manufacture 20,30 and 50% respectively of the total output. Of their outputs, 1, 3 and 5%, respectively, are defective. Ifa bolt is selected at random and found to be defective, C? what are the probabilities that it was manufactured by machine A, B or [13 marks]
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