3. (a) What is sample space? Using a real-life example, prove that sum of all probabilities should be 1. (b) A machine fills bags with a mixture of vegetables. Due to slight variation in the size of...

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Extracted text: 3. (a) What is sample space? Using a real-life example, prove that sum of all probabilities should be 1. (b) A machine fills bags with a mixture of vegetables. Due to slight variation in the size of vegetables, a set might be slightly underweight or overweight. A check of 4,000 sets in the past revealed: Event # sets Weight Underweight Satisfactory Overweight A 50 1800 C 150 What is the probability that a particular set will be either underweight or overweight? Make a comment.