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
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 28EQ
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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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