Question

In: Statistics and Probability

Show all of your work. No credit will be given if there is no work. Simplify...

Show all of your work. No credit will be given if there is no work. Simplify if possible, unless noted.

Setup:

• Suppose the probability of a part being manufactured by Machine A is 0.4

• Suppose the probability that a part was manufactured by Machine A and the part is defective is 0.12

• Suppose the probability that a part was NOT manufactured by Machine A and the part IS defective is 0.14

Questions To Answer: 1. (2 pts) Find the probability that a part is defective given that it was made by Machine A.

2. (2 pts) Find the probability that a part is defective.

3. (4 pts) Are the states of a part being made by Machine A and being defective independent? Circle your answer and state your reason. YES, they are independent NO, they are NOT independent Reason:

4. (2 pts) Find the probability that Machine A produced a specific part, given that the part was defective. Round your final answer to 2 decimals, if needed.

Solutions

Expert Solution

It is given that

the probability of a part being manufactured by Machine A is 0.4

Let us consider it as P(A)=0.4

using the sum of probabilities we will find the probability of part not being manufactured by machine A which is taken as

the probability that a part was manufactured by Machine A and the part is defective is 0.12

probability that a part was NOT manufactured by Machine A and the part is defective is 0.14

We have to determine the probability that a part is defective given that it was made by Machine A.

That will be P(D/A)

Use the conditional probability formula

We have to find the probability that part is defective

Probability that part is defective is 0.132

We have to check weather part manufactured by machine A and being defective are independent or not.

For independent it should follow the rule of probability

P(D and A)=P(D).P(A)=P(D/A).P(A)

P(D and A)=0.12

P(D)=0.132

P(D/A)=0.3

Here

P(A)=0.4

So part being defective and produced by machine A are not independent of each other

We have to find that machine A produces specific part and it is given that being defective

We have to find that

orchestra answered 10 months ago

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