A chip company has two manufacturing plants. Plant A produces 40% of the chips and Plant B produces 60% of the chips produced by the company. The company knows that 2% of the chips produced by plant A are defective and 1% of the chips produced by plant B are defective. If a randomly chosen chip produced by the company is defective, what is the likelihood that the chip came from plant A

P(A/D) = 0.5714

Step-by-step explanation:

Let's call A the event that a chip is produced by Plant A, B the event that a chip is produced by Plant B and D the event that the chip is defective

So, the likelihood or probability P(A/D) that a chip came from plant A given that the chip is defective is calculated as:

P(A/D) = P(A∩D)/P(D)

Where P(D) = P(A∩D) + P(B∩D)

Then, the probability P(A∩D) that a chip is produced by plant A and it is defective is calculated as:

P(A∩D) = 0.4*0.02 = 0.008

Because, Plant A produces 40% of the chips and 2% of the chips produced by plant A are defective.

At the same way, the probability P(B∩D) that a chip is produced by plant B and it is defective is calculated as:

P(B∩D) = 0.6*0.01 = 0.006

So, P(D) and P(A/D) are equal to:

P(D) = 0.008 + 0.006 = 0.014

P(A/D) = 0.008/0.014 = 0.5714

it means that if a randomly chosen chip produced by the company is defective, the likelihood that the chip came from plant A is 0.5714

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3