Question

Suppose frozen foods are packaged on three lines, where the final process is to place the expiration dates. Line a handles 29% of the production and fails to place the date on 1 out of 200 boxes; line b places the date on 56% of the boxes and fails to place it 1% of the time; and line c, omits the date on 1 out of 50 boxes. If a box with no expiration date is found, what is the probability that it was produced by line a? Note: use four decimal places in your answer.

          Suppose frozen foods are packaged on three lines, where the final process is to place the expiration dates. Line a handles 29% of the production and fails to place the date on 1 out of 200 boxes; line b places the date on 56% of the boxes and fails to place it 1% of the time; and line c, omits the date on 1 out of 50 boxes. If a box with no expiration date is found, what is the probability that it was produced by line a? Note: use four decimal places in your answer.
        
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Elementary Statistics a Step by Step Approach
Elementary Statistics a Step by Step Approach
Allan G. Bluman 9th Edition
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Suppose frozen foods are packaged on three lines, where the final process is to place the expiration dates. Line a handles 29% of the production and fails to place the date on 1 out of 200 boxes; line b places the date on 56% of the boxes and fails to place it 1% of the time; and line c, omits the date on 1 out of 50 boxes. If a box with no expiration date is found, what is the probability that it was produced by line a? Note: use four decimal places in your answer.
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Transcript

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00:01 In this question, we have a sugar production line.
00:05 There are two lines.
00:06 Line 1 produces twice as many bags as line 2, and the probability of a defective bag in line 1 is 0 .01.
00:14 Defective bag in line 2 is probability is 0 .03.
00:18 And the bag is randomly chosen in part a.
00:20 We want to find the probability the bag came from line 1.
00:24 Now, since line 1 produces twice as many as line 2, so in total there will be three parts and line 2 will produce 2 parts and line 1 will produce 1 part so it's 2 3rds or 0 .6667 4 decimal place okay part b in part b the probability of the back being defective it will have to be split into two mutually exclusive case first case is the back comes from line 1 and defective or now probability n is times notation wise is intercept.
01:19 All is plus notation wise is union.
01:21 So all is plus.
01:25 The back comes from line 2 and defective.
01:31 Okay, let's look at our first case.
01:33 It came from line 1, so 2 3 chance.
01:37 Now n will be times defective.
01:39 Now line 1 defective is 0 .01.
01:45 Now probability of line 2 will be 1 3rd, and defective...
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