Acomputer assembling company receives 24% of parts from supplier x, 36% of parts from supplier y, and the remaining 40% of parts from supplier z. five percent of parts supplied by x, ten percent of parts supplied by y, and six percent of parts supplied by z are defective. if an assembled computer has a defective part in it, what is the probability that this part was received from supplier z?

There is a 33% probability that this party was received from supplier Z.

Step-by-step explanation:

This can be formulated as the following problem:

What is the probability of B happening, knowing that A has happened.

It can be calculated by the following formula

Where P(B) is the probability of B happening, P(A/B) is the probability of A happening knowing that B happened and P(A) is the probability of A happening.

-In your problem, we have:

P(A) is the probability of a defective part being supplied. For this probability, we have:

In which is the probability that the defective product was chosen from supplier X(we have to consider the probability of supplier X being chosen). So:

is the probability that the defective product was chosen from supplier Y(we have to consider the probability of supplier Y being chosen). So:

is the probability that the defective product was chosen from supplier Z(we have to consider the probability of supplier Z being chosen). So:

So

P(B) is the probability of the supplier chosen being Z, so P(B) = 0.4

P(A/B) is the probability of the part supplied being defective, knowing that the supplier chosen was Z. So P(A/B) = 0.06.

So, the probability that this part was received from supplier Z is:

There is a 33% probability that this party was received from supplier Z.

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

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