Given and prove Statement and reason

Two types of defects are observed in the production of integrated circuit boards. It is estimated that 6% of the boards have sol

aalyn [17]

Answer:

(a) 0.09

(b) 0.06

(c) 0.0018

(d) 0.9118

(e) 0.03

Step-by-step explanation:

Let A = boards have solder defects and B = boards have surface defects.

The proportion of boards having solder defects is, P (A) = 0.06.

The proportion of boards having surface-finish defects is, P (B) = 0.03.

It is provided that the events A and B are independent, i.e.

$P(A\cap B)=P(A)\times P(B)$

(a)

Compute the probability that either a solder defect or a surface-finish defect or both are found as follows:

= P (A or B) + P (A and B)

$=P(A)+P(B)-P(A\cap B)+P(A\cap B)\\=P(A)+P(B)\\=0.06+0.03\\=0.09$

Thus, the probability that either a solder defect or a surface-finish defect or both are found is 0.09.

(b)

The probability that a solder defect is found is 0.06.

(c)

The probability that both defect are found is:

$P(A\cap B)=P(A)\times P(B)\\=0.06\times0.03\\=0.0018$

Thus, the probability that both defect are found is 0.0018.

(d)

The probability that none of the defect is found is:

$P(A^{c}\cup B^{c})=1-P(A\cup B)\\=1-P(A)-P(B)+P(A\cap B)\\=1-P(A)-P(B)+[P(A)\times P(B)]\\=1-0.06-0.03+(0.06\times0.03)\\=0.9118$

Thus, the probability that none of the defect is found is 0.9118.

(e)

The probability that the defect found is a surface finish is 0.03.

6 0

3 years ago

Convert 4x + 2y = 25 from standard form to slope intercept form Show your steps

Zigmanuir [339]

Answer:

y = -2x + 25/2

Step-by-step explanation:

Slope intercept form is y = mx + b.

You must solve the equation for y.

4x + 2y = 25

Subtract 4x from both sides.

2y = -4x + 25

y = -2x + 25/2

7 0

3 years ago

Can you explain how to solve this

Wewaii [24]

I believe it’s 180 or something to do with that

3 0

2 years ago

Kyla put 4 ounces of milk in 2 cups of coffee for her parents. How much milk would she need for 16 cups of coffee?A: 1cB: 1qtC:2

Ronch [10]

Kyla put 4 ounces of milk in 2 cups of coffee for her parents. How much milk would she need for 16 cups of coffee?

A: 1c

B: 1qt

C:2c

D:2qt

______________

4 ounces of milk in 2 cups of coffee for her parents.

4/2= 2 ounces of milk per cup

___________________

for 16 cups

Do you know how many ounces correspond to c or qt?

16* 2= 32 ounces

________________

32 ounces = 1 qt

So then,

Kyla needs to put 1 qt for 16 cups of coffee

Answer: B 1 qt

Do you have any questions regarding the solution?

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7 0

1 year ago

Use mathematical induction to prove that, for n ≥ 1, n³ – n is divisible by 3.

ICE Princess25 [194]

Answer:

Step-by-step explanation:

5 0

2 years ago