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Question 1 A biscuit factory has three machines used to pack biscuits into large boxes that are then sent out to supermarkets. The machines are labelled A, B, and C, and every day each machine packs many boxes of biscuits. The machines work at different speeds: from all the boxes produced on a given day 40% were packed by A, another 40% by B, and the remaining 20% by machine C. Some biscuits break during the packing process, which is a problem. Machine A does this quite a lot: for any box packed by A there is a probability 0.1 that it contains some broken biscuits. Machine B is better, with a probability 0.03 that a box from that machine will contain some broken biscuits. Machine C is best of all, with a probability of just 0.01 that a box it packs will have some broken biscuits. All of these probabilities are independent for every box. Before the boxes are sent out from the factory a few are picked out at random and checked to see whether they contain any broken biscuits. 1.1 What is the probability that a box contains some broken biscuits? 1.2 One of the boxes being checked does contain broken biscuits. What is the probability that it was packed by machine B? For each part include your working as well as the final answer. State any important results that you use in your calculation

Question 1 A biscuit factory has three machines used to pack biscuits into large boxes that are then sent out to supermarkets. The machines are labelled A, B, and C, and every day each machine packs many boxes of biscuits. The machines work at different speeds: from all the boxes produced on a given day 40% were packed by A, another 40% by B, and the remaining 20% by machine C. Some biscuits break during the packing process, which is a problem. Machine A does this quite a lot: for any box packed by A there is a probability 0.1 that it contains some broken biscuits. Machine B is better, with a probability 0.03 that a box from that machine will contain some broken biscuits. Machine C is best of all, with a probability of just 0.01 that a box it packs will have some broken biscuits. All of these probabilities are independent for every box. Before the boxes are sent out from the factory a few are picked out at random and checked to see whether they contain any broken biscuits. 1.1 What is the probability that a box contains some broken biscuits? 1.2 One of the boxes being checked does contain broken biscuits. What is the probability that it was packed by machine B? For each part include your working as well as the final answer. State any important results that you use in your calculation

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Question 1 A biscuit factory has three machines used to pack biscuits into large boxes that are then sent out to supermarkets. The machines are labelled A, B, and C, and every day each machine packs many boxes of biscuits. The machines work at different speeds: from all the boxes produced on a given day 40% were packed by A, another 40% by B, and the remaining 20% by machine C. Some biscuits break during the packing process, which is a problem. Machine A does this quite a lot: for any box packed by A there is a probability 0.1 that it contains some broken biscuits. Machine B is better, with a probability 0.03 that a box from that machine will contain some broken biscuits. Machine C is best of all, with a probability of just 0.01 that a box it packs will have some broken biscuits. All of these probabilities are independent for every box. Before the boxes are sent out from the factory a few are picked out at random and checked to see whether they contain any broken biscuits. 1.1 What is the probability that a box contains some broken biscuits? 1.2 One of the boxes being checked does contain broken biscuits. What is the probability that it was packed by machine B? For each part include your working as well as the final answer. State any important results that you use in your calculation.
Transcribed Image Text:Question 1 A biscuit factory has three machines used to pack biscuits into large boxes that are then sent out to supermarkets. The machines are labelled A, B, and C, and every day each machine packs many boxes of biscuits. The machines work at different speeds: from all the boxes produced on a given day 40% were packed by A, another 40% by B, and the remaining 20% by machine C. Some biscuits break during the packing process, which is a problem. Machine A does this quite a lot: for any box packed by A there is a probability 0.1 that it contains some broken biscuits. Machine B is better, with a probability 0.03 that a box from that machine will contain some broken biscuits. Machine C is best of all, with a probability of just 0.01 that a box it packs will have some broken biscuits. All of these probabilities are independent for every box. Before the boxes are sent out from the factory a few are picked out at random and checked to see whether they contain any broken biscuits. 1.1 What is the probability that a box contains some broken biscuits? 1.2 One of the boxes being checked does contain broken biscuits. What is the probability that it was packed by machine B? For each part include your working as well as the final answer. State any important results that you use in your calculation.
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