The production process of computer parts uses two machines one old & one new. If the old machine is used the probability that the defected part is produced is .13 if the new machine is used the probability that the defective part is produced is .04. moreover, the new machine produces parts 4 times as fast as the old machine does.
I am trying to draw a tree diagram to represent the above probabilities. I can't figure out what the .13 and .04 would be over?
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To draw a tree diagram representing the given probabilities, you need to consider the different possible outcomes at each stage of the process. In this case, there are two stages: choosing the machine (old or new) and producing a part (defective or non-defective).
Here's how you can draw the tree diagram:
First, draw two branches at the beginning to represent the two options for choosing the machine: old and new. Label these branches as "Old Machine" and "New Machine."
Next, for each machine, draw two more branches to represent the probabilities of producing a defective part or a non-defective part. Label these branches as "Defective" and "Non-defective."
Now, assign the probabilities given in the problem to the appropriate branches.
For the branch "Old Machine," assign the probability of producing a defective part, which is 0.13 (as given in the problem).
For the branch "New Machine," assign the probability of producing a defective part, which is 0.04 (as given in the problem).
Since the problem states that the new machine produces parts 4 times as fast as the old machine does, it means the new machine is 4 times more likely to make parts compared to the old machine. So, to represent this, you can assign a probability of 0.8 to the branch "Non-defective" under the "New Machine" branch.
Finally, in the last stage, you can label the remaining branches under "Old Machine" and "New Machine" as "Non-defective," and assign the probabilities 0.87 (1 - 0.13) and 0.96 (1 - 0.04) respectively.
Your tree diagram should now have two branches representing the two machines, and within each branch, two branches representing the production of defective or non-defective parts. The probabilities can be assigned as mentioned above.
Remember, a tree diagram can be a useful visual tool to represent the possible outcomes and probabilities of a multi-stage process.