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**Q1:**A new restaurant would like to investigate if different age groups of customers prefer different types of food items. Each of their customers is given a food item - a burger or a sandwich. Each customer belongs to either adult or child age group. The customers were then surveyed on whether they enjoyed the food item. The table below gives the percentage of customers in each category.See Answer**Q2:**Due to the small size of mobile screens, it is common for users to mistype their words when texting or emailing over phone. Hence, to increase the usability of the apps, it is important to automatically correct or suggest a corrected version of the mistyped words. We can identify the correct word in the following way. For a given mistyped word w, we can generate multiple candidate words that could be correct, and evaluate each candidate c using the Bayes' rule.See Answer**Q3:**1. Using one practical example, explain the decision-making process and all its stages. (30 marks)See Answer**Q4:**2. Explain how probability is useful in decision-making. (10 marks)See Answer**Q5:**3. Suggest in full any six benefits of strategic planning. (30 marks)See Answer**Q6:**4. Discuss the strategic planning perspectives and give examples of businesses that may engage in each. (30 marks)See Answer**Q7:**(a)The product rule (also called the chain rule)states that:P(X1,X2,,Xn)=P(X1)P(X2|X1)P(X3|X1,X2)..P(Xn|X1,X2,,Xn-1)Now,prove the above rule in reverse direction as stated below:P(X1)P(X2 I X1)P(X3 | X1,X2)...P(Xn|X1,X2,...Xn-1)=P(X1,X2,...,Xn)(b)Prove that zeDomain()P(A=B=b)=1,where Domain(A)represents all thevalues that the random variable A can take,and the random variable B is assigned toits value b.See Answer

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