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Ratling [72]
3 years ago
13

Assume that there is a 4​% rate of disk drive failure in a year. a. If all your computer data is stored on a hard disk drive wit

h a copy stored on a second hard disk​ drive, what is the probability that during a​ year, you can avoid catastrophe with at least one working​ drive? b. If copies of all your computer data are stored on four independent hard disk​ drives, what is the probability that during a​ year, you can avoid catastrophe with at least one working​ drive?
Mathematics
1 answer:
kap26 [50]3 years ago
7 0

Answer:

a) 99.84% probability that during a​ year, you can avoid catastrophe with at least one working​ drive

b) 99.999744% probability that during a​ year, you can avoid catastrophe with at least one working​ drive

Step-by-step explanation:

For each disk drive, there are only two possible outcomes. Either it works, or it does not. The disks are independent. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

4​% rate of disk drive failure in a year.

This means that 96% work correctly, p = 0.96

a. If all your computer data is stored on a hard disk drive with a copy stored on a second hard disk​ drive, what is the probability that during a​ year, you can avoid catastrophe with at least one working​ drive?

This is P(X \ geq 1) when n = 2

We know that either none of the disks work, or at least one does. The sum of the probabilities of these events is decimal 1. So

P(X = 0) + P(X \geq 1) = 1

We want P(X \geq 1). So

P(X \geq 1) = 1 - P(X = 0)

In which

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{2,0}.(0.96)^{0}.(0.04)^{2} = 0.0016

P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0016 = 0.9984

99.84% probability that during a​ year, you can avoid catastrophe with at least one working​ drive

b. If copies of all your computer data are stored on four independent hard disk​ drives, what is the probability that during a​ year, you can avoid catastrophe with at least one working​ drive?

This is P(X \ geq 1) when n = 4

We know that either none of the disks work, or at least one does. The sum of the probabilities of these events is decimal 1. So

P(X = 0) + P(X \geq 1) = 1

We want P(X \geq 1). So

P(X \geq 1) = 1 - P(X = 0)

In which

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{4,0}.(0.96)^{0}.(0.04)^{4} = 0.00000256

P(X \geq 1) = 1 - P(X = 0) = 1 - 0.00000256 = 0.99999744

99.999744% probability that during a​ year, you can avoid catastrophe with at least one working​ drive

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EXERC
eimsori [14]

Answer:551.3212cm³

Step-by-step explanation:

Find the image attached

The volume is made up of a cone, cylinder and a hemisphere

Volume of the shape = Volume of cone + volume of cylinder + volume of hemisphere

Get the volume of the cone;

Volume of a cone Vc = 1/3πr²h

r is the base radius = 3.5cm

Height = 10cm

Vc = 1/3π(3.5)²(6)

Vc = 1/3π(12.25)(6)

Vc = 12.25 * 2π

Vc = 24.5π cm³

Get the volume of the cylinder;

Vcy = πr²h

r = 3.5cm

h = 10cm

Vcy = π(3.5)²(10)

Vcy = π(12.25)(10)

Vcy = π(122.5)

Vcy = 122.5π cm³

Get rhe volume of the hemisphere;

Volume of hemisphere = 2/3 πr³

r = 3.5cm

Vh =  2/3 π(3.5)³

Vh = 2/3π(42.875)

Vh = 28.58π cm³

Volume of the shape = VC + Vcy + Vh

Volume of the shape = 24.5π+122.5π+28.58π

Volume of the shape = 175.58π

<em>Volume of the shape = 551.3212cm³</em>

7 0
3 years ago
WILL GIVE BRAINLEST plz help meeeeeeeee
mixer [17]

Answer:

4

Step-by-step explanation:

3 0
3 years ago
What is the value of x in the equation 3- 2x = -1.5х?
Vika [28.1K]

Answer:

x = 6

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

Equality Properties

Step-by-step explanation:

<u>Step 1: Define Equation</u>

3 - 2x = -1.5x

<u>Step 2: Solve for </u><em><u>x</u></em>

  1. Add 2x on both sides:                    3 = 0.5x
  2. Divide 0.5 on both sides:               6 = x
  3. Rewrite:                                           x = 6

<u>Step 3: Check</u>

<em>Plug in x into the original equation to verify it's a solution.</em>

  1. Substitute in<em> x</em>:                    3 - 2(6) = -1.5(6)
  2. Multiply:                               3 - 12 = -9
  3. Subtract:                              -9 = -9

Here we see that -9 does indeed equal -9.

∴ x = 6 is the solution to the equation.

6 0
2 years ago
Read 2 more answers
What are the values for the coefficients and constant term of 2 + 3x² - 5x?<br> a=<br> B=<br> C=
Aleks [24]

Answer:

a=3

b=-5

c=2

Step-by-step explanation:

Because first arrange them in decreasing order by their variables powers like this 3x²-5x+2 after that take the the coefficients

5 0
2 years ago
A and B are two events. Which statement about the conditional probability is true?
nata0808 [166]
The answer 
by using fundamental definition
<span>The conditional probability of event B given event A is P(B|A)=P(A and B)/P(A) when two events are not independent.
so the only true answer is A, because </span>P(B|A)=P(A) if A and B are independents<span>
(definition)</span>
4 0
3 years ago
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