Questions: Ryan is a quality control inspector who works at a factory that produces inexpensive, unassembled furniture. He has a batch of plastic connection parts to inspect. Suppose 145 of these parts will not pass inspection and there are 1000 parts total in the batch. Ryan chooses a plastic connection part to inspect at random. Let the event A and the event B be as follows. A: The part Ryan chooses does not pass inspection. B: The part Ryan chooses passes inspection. Find the following probabilities. Write your answers as decimal numbers and do not round. P(A)= P(B)=

Ryan is a quality control inspector who works at a factory that produces inexpensive, unassembled furniture. He has a batch of plastic connection parts to inspect. Suppose 145 of these parts will not pass inspection and there are 1000 parts total in the batch.

Ryan chooses a plastic connection part to inspect at random. Let the event A and the event B be as follows. A: The part Ryan chooses does not pass inspection. B: The part Ryan chooses passes inspection. Find the following probabilities. Write your answers as decimal numbers and do not round.

P(A)=

P(B)=

Transcript text: Ryan is a quality control inspector who works at a factory that produces inexpensive, unassembled furniture. He has a batch of plastic connection parts to inspect. Suppose 145 of these parts will not pass inspection and there are 1000 parts total in the batch. Ryan chooses a plastic connection part to inspect at random. Let the event $A$ and the event $B$ be as follows. A: The part Ryan chooses does not pass inspection. B: The part Ryan chooses passes inspection. Find the following probabilities. Write your answers as decimal numbers and do not round. \[ P(A)= \] \[ P(B)= \]

Solution

Solution Steps

Step 1: Identify the total number of parts and the number of defective parts

The total number of parts in the batch is $ 1000 $. Out of these, $ 145 $ parts do not pass inspection.

Step 2: Calculate $ P(A) $, the probability that a randomly chosen part does not pass inspection

The probability $ P(A) $ is calculated as the ratio of the number of defective parts to the total number of parts: \[ P(A) = \frac{\text{Number of defective parts}}{\text{Total number of parts}} = \frac{145}{1000} = 0.145 \]

Step 3: Calculate $ P(B) $, the probability that a randomly chosen part passes inspection

The probability $ P(B) $ is calculated as the ratio of the number of non-defective parts to the total number of parts. Since $ 145 $ parts are defective, the number of non-defective parts is $ 1000 - 145 = 855 $: \[ P(B) = \frac{\text{Number of non-defective parts}}{\text{Total number of parts}} = \frac{855}{1000} = 0.855 \]

Final Answer

$ P(A) = \boxed{0.145} $
$ P(B) = \boxed{0.855} $

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