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larisa86 [58]
3 years ago
15

In a test of a printed circuit board using a random test pattern, an array of 14 bits is equally likely to be 0 or 1. Assume the

bits are independent.
(a) What is the probability that all bits are 1s? Round your answer to six decimal places (e.g. 98.765432). Enter your answer in accordance to the item a) of the question statement
(b) What is the probability that all bits are 0s? Round your answer to six decimal places (e.g. 98.765432). Enter your answer in accordance to the item b) of the question statement
(c) What is the probability that exactly 7 bits are 1s and 7 bits are 0s? Round your answer to three decimal places (e.g. 98.765). Enter your answer in accordance to the item c) of the question statement
Mathematics
1 answer:
dangina [55]3 years ago
7 0

Answer:

(a) 0.000061

(b) 0.000061

(c) 0.209

Step-by-step explanation:

An array of 14 bits is equally likely to be 0 or 1.

That is, P (0) = P (1) = 0.50.

(a)

Compute the probability that all bits are 1s as follows:

P(\text{All bits are 1s})=[P(1)]^{14} ∵ the bits are independent

                            =(0.50)^{14}\\=0.00006103515625\\\approx 0.000061

Thus, the probability that all bits are 1s is 0.000061.

(b)

Compute the probability that all bits are 0s as follows:

P(\text{All bits are 0s})=[P(0)]^{14} ∵ the bits are independent

                            =(0.50)^{14}\\=0.00006103515625\\\approx 0.000061

Thus, the probability that all bits are 0s is 0.000061.

(c)

Compute the probability that exactly 7 bits are 1s and 7 bits are 0s as follows:

Define <em>X</em> as the number of bits that 1s.

Then the random variable <em>X</em> will follows a binomial distribution with parameters <em>n</em> = 14 and <em>p</em> = 0.50.

The value of P (X = 7) is:

P(X=7)={14\choose 7}(0.50)^{7}(1-0.50)^{14-7}

               =\frac{14!}{7!\times 7!}\times (0.50)^{14}\\\\=3432\times 0.000061\\\\=0.209352\\\\\approx 0.209

Thus, the probability that exactly 7 bits are 1s and 7 bits are 0s is 0.209.

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Given:

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Answer:

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Step-by-step explanation:

Let x denote the length of the dog run and y denote the width of the dog run.

Given that the garage wall serves as one side of the dog run, we are left with 3 other sides to instal the fence.

Carrie has 180ft of fencing with her, so the sum of the lengths of the 3 sides has to be equal to 180. We can represent this in the form of an equation as

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The area enclosed will be equal to the length multiplied with the width. So,

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The fence encloses 3600 sq ft.


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3 years ago
In the isosceles triangle, find a and b if you knew the perimeter was 20x+35
Zanzabum

Answer:

a=8

b=17

Step-by-step explanation:

Isoceles means we will have 2 congruent sides in this triangle.

So it appears we are to assume it is sitting on its base which means that other side has measurement ax+9 as well

So we have the sum of the 3 sides is the perimeter.

That means we have the equation:

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Subtract 18 on both sides:

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Answer:

Hi...

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So...b=137/4

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