Suppose that the space shuttle has three separate computer control systems: the main system and two backup duplicates of it. The first backup would monitor the main system and kick in if the main system failed. Similarly, the second backup would monitor the first. We can assume that a failure of one system is independent of a failure of another system, since the systems are separate. The probability of failure for any one system on any one mission is known to be 0.01.
(a) Find the probability that the shuttle is left with no computer control system on a mission. (Enter your answer to six decimal places.)
(b) How many backup systems does the space shuttle need if the probability that the shuttle is left with no computer control system on a mission must be
1
one hundred thousand
(Enter your answer as a whole number.)
_____ backup systems.

Answers

Answer 1

Answer:

a) 0.000001 = 0.0001% probability that the shuttle is left with no computer control system on a mission.

b) 3 backup systems are needed.

Step-by-step explanation:

For each system, there are only two possible outcomes. Either it works, or is does not. Systems are independent. This means that 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.

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

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

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Three separate computer control systems

This means that [tex]n = 3[/tex]

The probability of failure for any one system on any one mission is known to be 0.01.

So the probability of working is:

[tex]p = 1 - 0.01 = 0.99[/tex]

(a) Find the probability that the shuttle is left with no computer control system on a mission. (Enter your answer to six decimal places.)

This is [tex]P(X = 0)[/tex]

So

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

[tex]P(X = 0) = C_{3,0}.(0.99)^{0}.(0.01)^{3} = 0.000001[/tex]

0.000001 = 0.0001% probability that the shuttle is left with no computer control system on a mission.

(b) How many backup systems does the space shuttle need if the probability that the shuttle is left with no computer control system on a mission must be 1 over one hundred thousand

This is n for which:

[tex]P(X = 0) < \frac{1}{100000} = 0.00001[/tex]

With 2 backup systems, the probability is lower than this, so lets see if with only two is possible.

We find [tex]P(X = 0)[/tex] when [tex]n = 2[/tex]. So

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

[tex]P(X = 0) = C_{2,0}.(0.99)^{0}.(0.01)^{2} = 0.0001 > 0.00001[/tex]

So 3 backup systems are needed.


Related Questions

Solve the problem:

The number of inhabitants in millions of a certain city can be calculated using the expression [tex]p (x) = 2^{3} * 10\frac{2t}{3}[/tex] If t represents time in years:

a) How long approximately must elapse for the population of the city to be 200 million inhabitants?

b) How many inhabitants will be in the city after 4 years?

Answers

Answer:

Given function:

p(t) = 2³[tex]10^{2t/3}[/tex]

a)

Find x when p(t) = 200:

2³[tex]10^{2t/3}[/tex] = 200[tex]10^{2t/3}[/tex] = 2522t/3 = log 25t = 3 log 5t = 2.0969 years ≈ 2 years and 1 month

b)

Find p(t) when t = 4:

p(4) = 2³([tex]10^{2*4/3}[/tex] ) = 8*[tex]10^{8/3}[/tex] = 3713.27 million

i need help and fast hurry! im not joking!

Answers

Last one is incorrect, it is shade 6 of the 8 unites. Everything else looks fine.

The graph of f(x) = x2 was transformed tu
create the graph of d(x) = f(x) + 9. Which of
the following attributes will be the same for the
graphs f(x) and d(x)?
1. the domain
11. the range
III. the axis of symmetry

Answers

Answer:

i: the domain.

iii: the axis of symmetry.

Step-by-step explanation:

We have the function:

f(x) = x^2

The domain of this function is the set of all real numbers, and the range is:

R: [0, ∞)

(because 0 is the minimum of x^2)

Now we have the transformation:

d(x) = f(x) + 9 = x^2 + 9

Notice that this is only a vertical translation of 9 units, then there is no horizontal movement, then the axis of symmetry does not change.

Also, in d(x) there is no value of x that makes a problem, so the domain is the set of all real numbers, then the domain does not change.

And d(x) = x^2 + 9 has the minimum at x = 0, then the minimum is:

d(0) = 0^2 + 9 = 9

Then the range is:

R: [9,  ∞)

Then the range changes.

So we can conclude that the attributes that will be the same for f(x) and d(x) are:

i: the domain.

iii: the axis of symmetry.

Find the surface area of the following prism:
6 m
6 m
10 m
7.2 m
4.8 m

Answers

Answer:

172.8m³

Step-by-step explanation:

1/2(7.2)(4.8)(10)=172.8m³

To stay in a hotel it costs $104 each night (n) plus a $15 fee for parking. Think of the linear function that demonstrates the total cost (C) of staying in the hotel in terms of the number of nights (n) stayed. whats the initial value ? ​

Answers

Answer:

the equation is:    (104 * x) + 15 = y     i believe

Step-by-step explanation:

104 OF THE NUMBER of nights so times x because you dont know the number

and + 15 because of the fee

1. How many sixths do you need to make one whole unit?

Answers

Answer:

6

Step-by-step explanation:

you need 6/6 to make 1

if theres a pie cut 6 times you need all 6 pieces to make it whole again

Answer:

1/6 is one and to make one whole you need 6

Step-by-step explanation:

Please help I think it’s 4.0cm2 I’m i right?

Answers

Answer:

yes u are right give me brainlest plzzzzzzzzzzzzzzzzzzzzzzzzzz

Step-by-step explanation:

4.5m + 8 - 2.3m - 3.5

Answers

Answer:

494235234934-1304039445

Step-by-step explanation:

4r567890e-r0987ytdghcn

1. Which solid has one base that is a rectangle and four lateral surface that are triangles?
A- Triangular Pyramid
B- Cone
C- Rectangular Prism
D- Rectangular Pyramid

2. A solid with at most one base CANNOT be which of the following?
A- Cone
B- Cube
C- Pyramid
D- Sphere

Answers

1. Triangular prism
2. Sphere i think

A digital communication channel transmits bits of information, usually designated as 0 and 1. If a sender transmits a 0, he/she hopes the recipient receives a 0. If a sender transmits a 1, he/she hopes that the recipient receives a 1. Unfortunately, this is not always the case. Suppose on a certain transmission line, a transmitted 0 is received correctly 90% of the time (10% of the time a 1 is received), and a transmitted 1 is received correctly 74% of the time. (26% of the time a 0 is received.) It is known that on this transmission line, 80% of all bits transmitted are 0 bits. A randomly selected transmitted bit is examined. Say its value is X. The bit received is Y. a.What is the probability that X

Answers

Answer:

a) 0.80

b) 0.72

c) 0.02

Step-by-step explanation:

It is assumed that

X = Bit transmitted

Y = Bit received

[tex]X^{0}[/tex] = Transmissted bit is 0

[tex]X^{1}[/tex] = Transmissted bit is 1

[tex]Y^{0}[/tex] = Received bit is 0

[tex]Y^{1}[/tex] = Received bit is 1

As per the given condition

P [ [tex]Y^{0}[/tex] | [tex]X^{0}[/tex] ] = 90%

P [ [tex]Y^{0}[/tex] | [tex]X^{1}[/tex] ] = 100% - 90% = 10%

P [ [tex]Y^{1}[/tex] | [tex]X^{1}[/tex] ] = 74%

P [ [tex]Y^{0}[/tex] | [tex]X^{0}[/tex] ] = 100% - 74% = 26%

P [ Tramitted bits are 0 ] = 80%

Now calculate each situation

a)

As all the transmitted bits are o has possibilit of 80% then

P [ X = 0 ] = P [ [tex]X^{0}[/tex] ] = 80% = 0.80

b)

P [ X = 0, Y = 0 ] = P [ [tex]X^{0}[/tex] , [tex]Y^{0}[/tex] ] = P [ [tex]Y^{0}[/tex] | [tex]X^{0}[/tex] ] x P [ [tex]X^{0}[/tex] ]  = 90% x 80% = 72% = 0.72

c)

P [ X = 1, Y = 0 ] = P [ [tex]X^{1}[/tex] , [tex]Y^{0}[/tex] ] = P [ [tex]Y^{0}[/tex] | [tex]X^{1}[/tex] ] x P [ [tex]X^{1}[/tex] ]  = 10% x ( 100% - 80% ) = 10% x 20% = 2% = 0.02

For a school fundraiser Paul bought a big box of ducks and wrote prize amounts, in dollars on the bottom of each rubber duck. The prize amounts were $5, $10, $20, $50, and$100. The number of ducks with each prize amount varied so that the total value for all the ducks with each prize amount was always $500. Paul then put all of the rubber ducks in his schools swimming pool. At the fundraiser participants used a long net to catch a duck from the pool. They won the amount written on the bottom of the duck, and then they threw the duck back into the pool before the next persons turn. Since the ducks were returned to the pool after they were caught the chances of winning any particular amount remained the same. Andrew paid $15 to play the game once. If we assume he randomly selected a duck, what is the probability that Andrew won more money than he paid to play the game?

Answers

Answer:

Redding East Rotary donates 120 holiday baskets every year. ... Frank was $50 proud. ... Please turn in your tickets and money to Bill Evanhoe directly this year. ... The door prize of $20 to San Francisco Deli was won by Carla Barrett. ... The Duck Derby has raised $3,515,000 and if you put all those ducks end to end they ...

Step-by-step explanation:

Y gg tucks he go F hjjiioi

How does 39.54 compare to 39.4

Answers

Answer:

39.54 is greater than 39.4

Step-by-step explanation:

Answer:

39.54 is LESS than 39.4

Highlight all of the Like Terms on questions 1-2 please!! (any color) (due in 5 minutes)

Answers

Answer:

1. 8,13,8,3,g

2. 8,13,3,g (Like term pair 1) and 8 (Like term pair 2)

Step-by-step explanation:

simplify -2+5(2+6r)

I’ll mark brainlist

Answers

Answer:

10+30r

Step-by-step explanation:

-2+5(2+6r)

expand 5(2+6r)

5x2=10

(6r)x(5)=30r

so it is 10+30r

then add that to -2

8+30r

Hope that helps :)

What is the y intercept of a line that passes through the points (2, -2.5) and (4, -2)

Answers

Answer:

-3

Step-by-step explanation:

To find the slope of this line, you have to subtract that first y coordinate from the second y coordinate, and divide that by the quantity equal to the second x coordinate minus the first.

-2 - -2.5 = 0.5

4 - 2 = 2

0.5/2 = 1/4

Now you plug in the info you already have into a y=mx+b format. Chose one of the pairs of coordinates given in instruction to be the x and y values.

-2 = 1/4(4) + b

-2 = 1 + b

-3 = b

-3 is the y-intercept.

11 - 5x + 4x + 2 = 13 - 1x
True or False?

Answers

Answer:

True

Step-by-step explanation:

Simplify the left side. Combine like terms (terms with the same amount of variables).

11 + 2 = 13

-5x + 4x = 4x - 5x = -x

-x + 13 = 13 - x (True)

True is your answer.

~

Seven times the difference of a number and 7

Answers

Answer:

7 (x-7) or 7x-49

7x-49 would be the answer

what is an equivalence class?

Answers

This article is about equivalency in mathematics. For equivalency in music, see equivalence class (music).

Congruence is an example of an equivalence relation. The leftmost two triangles are congruent, while the third and fourth triangles are not congruent to any other triangle shown here. Thus, the first two triangles are in the same equivalence class, while the third and fourth triangles are each in their own equivalence class.

In mathematics, when the elements of some set S have a notion of equivalence (formalized as an equivalence relation) defined on them, then one may naturally split the set S into equivalence classes.

                              The information is from https://en.wikipedia.org/wiki/Equivalence_class

                         If it is wrong I am sorry

Write the equation in standard form for the circle x^2 + y^2 - 14y + 24 = 0

Answers

Answer:

x^2+(y-7)^2=25

Step-by-step explanation:

x^2+y^2-14y=-24

x^2+(y-7)^2-49=-24

x^2+(y-7)^2=25

Solve the equation for y: 2 y – 25 = 19

Answers

Answer:

2y - 25 = 19

2y = 19 + 25

2y = 44

y = 44 / 2

y = 22

Hope it helps

45 is what percent of 9

i have to show work

Answers

Answer:

500%

Step-by-step explanation:

45 divided by 9 x 100 = 500

Answer:

20%

Step-by-step explanation:

1) Calculate fraction's value.

2) Multiply that number by 100.

3) Add the percent sign % to it.

Simplify 3(r+5)-4r help me pls NOW

Answers

Answer:

-r + 15

Step-by-step explanation:

3r + 15 - 4r =

-r + 15

Hope that helps!

In AHIJ, the measure of J=90°, IJ = 5 feet, and JH = 3.2 feet. Find the measure of
I to the nearest tenth of a degree.
5
J
H
3.2

Answers

Answer:33.6

Step-by-step explanation:

Answer:

32.6

Step-by-step explanation:

Bentley had 17 pencils. Kerry
had 32 pencils. How many
more pencils does Kerry have
than Bentley?

Answers

Kerry has 15 more pencils.
Question:-

Bentley had 17 pencils. Kerry

had 32 pencils. How many

more pencils does Kerry have

than Bentley?

Solution:-

Number of pencils Bentley had = 17 pencils.

Number of pencils Karry had = 32 pencils.

Number of pencils Karry have more than Bentley = 32 - 17 = 15

Answer:-

Karry have 15 pencils more than Bentley.

With
Sue buys a car costing £8000 plus
20% VAT.
She pays £4000 deposit and then
chooses to pay the balance in ten equal
monthly payments.
Calculate each monthly payment
CS

Answers

Answer:

Each monthly payment is of £560.

Step-by-step explanation:

Sue buys a car costing £8000 plus 20% VAT?

She has to pay:

8000 plus 20% of tax. So

[tex]T = 8000 + 0.2*8000 = 9600[/tex]

She pays £4000 deposit and then chooses to pay the balance in ten equal monthly payments.

4000 deposit, and then 9600 - 4000 = 5600 divided in ten equal monthly payments.

5600/10 = 560

Each monthly payment is of £560.

Solve the equation below. 2.3=p+0.6p=

Answers

Answer:

p=1.4375

Step-by-step explanation:

Elijah has a loyalty card good for a discount at his local grocery store. The item he
wants to buy is priced at $44, before discount and tax. After the discount, and before
tax, the price is $40.92. Find the percent discount.

Answers

Answer:

7%

Step-by-step explanation:

In ANOP, the measure of ZP=90°, the measure of ZN=26°, and OP = 13 feet. Find
the length of PN to the nearest tenth of a foot.



Answers

Answer:

Length of PN = 26.65 ft (Approx.)

Step-by-step explanation:

Given:

In ΔNOP

∠ P = 90°

∠ N = 26°

OP = 13 ft

Find:

Length of PN

Computation:

using trigonometry application

Tan 26 = 13 / PN

0.4877 = 13 / PN

Length of PN = 26.65 ft (Approx.)

B = I(1 + r)2(1 + r) = I(1 + r)3 What pattern is forming?

Answers

Th answer is 2r+7t-32

What comes next ? Finish the pattern 618427

Answers

5039 that’s the answer I think I could be wrong

The value of the number is 4.

Given to us

Series = {6,1,8,4,2,7}

Assumption

Let the next number in the series be x.

Patterns

looking at the pattern the series can be classified into two

odd series consisting of the numbers {6, 8, 2, x}even series consisting of the numbers {1, 4, 7}

Odd Series

As the x is falling under the odd number series the,

we can see the difference in the odd series is following -2, +6, -2, +6; therefore, following the same series we get

6 + 2 = 8

8 - 6 = 2

2 + 2 = 4

Hence, the value of the number is 4.

Learn more about series and sequence:

https://brainly.com/question/8195467

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