1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Ede4ka [16]
3 years ago
10

A satellite system consists of n components and functions on any given day if at least k of the n components function on that da

y. On a rainy day, each of the components independently functions with probability p1, whereas on a dry day, each independently functions with probability p2. If the probability of rain tomorrow is α, what is the probability that the satellite system will function?
Mathematics
1 answer:
Charra [1.4K]3 years ago
4 0

Answer:

P = αP(x≥k,p1) + (1-α)P(x≥k,p2)

Step-by-step explanation:

The probability that k of n components function on a day follows a binomial distribution, so the probability is:

P(k,p)=nCk*p^{k}*(1-p)^{n-k}

Where p is the probability that a component function and nCk is \frac{n!}{k!(n-k)!}

So, the probability that at least k of the n components function on a day is:

P(x≥k,p) = P(k,p) + P(k+1,p) + P(k+2,p) + ... + P(n,p)

Then, if it is rain, the probability of the function p is equal to p1, if it isn't the probability p is equal to p2, so the probability P that the satellite system will function is:

P = αP(x≥k,p1) + (1-α)P(x≥k,p2)

Where, P(x≥k,p1) and P(x≥k,p2) are equal to:

P(x≥k,p1) = P(k,p1) + P(k+1,p1) + P(k+2,p1) + ... + P(n,p1)

P(x≥k,p2) = P(k,p2) + P(k+1,p2) + P(k+2,p2) + ... + P(n,p2)

You might be interested in
The diameter of a circle pass through
Neko [114]
The diameter of a circle passes through the middle
8 0
3 years ago
Confused ???????????
suter [353]
The last one because its like turning it into a fraction but your putting as a desamile or how ever you spell it
4 0
3 years ago
Plz Answer this ASAP <br>Select the statement that is true.
g100num [7]

The maximum height is 64ft and the ballon is only in the air for 2 seconds

6 0
3 years ago
Read 2 more answers
I need help what is 3.45 x (-2.8)<br> please show steps
guajiro [1.7K]

gShbtep-by-step explanajtiottdhjbgbfgtvjhjnjh:ttttt

3 0
2 years ago
Kun-cha has 150 feet of fencing to make a corral for her horses. The barn will be one side of the partitioned rectangular enclos
Assoli18 [71]
So to graph you problem you should first consider that the one side of the bar is 150feet because it is in the other partitioned of the fence and the function of it would be 150(x) because the barn's area is calculated through it length time width. I hope this will help 
3 0
3 years ago
Other questions:
  • A rectangle on a coordinate plane has vertices Q(Negative 1, 1), R(6, 1), S(6, Negative 8), and T(Negative 1, Negative 8). What
    9·1 answer
  • Jose wants to find the cost of sales tax rewrite the formula to solve for the percent sales tax
    13·1 answer
  • Whats the slope of (5,4) and (7,8)​
    14·2 answers
  • 5 = x is the same as x = 5 due to what
    6·2 answers
  • Can I get an explanation on how to do this?
    6·2 answers
  • What is the area of the shaded region in the figure? Hurry please!!!! And please answer with no links, thanks!!
    14·2 answers
  • -6n + 3= 45<br><br>how do solve this? I need help showing my work<br>​
    12·1 answer
  • The tax rate for Regina’s purchase is 8.75%. How much money did Regina spend at the store.
    14·2 answers
  • The probability that a school wins their first game in the national college basketball tournament is related to the rank they ha
    11·1 answer
  • Need help with my homework plz
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!