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
Help me do question 1. 2. and 3. for 100 points and brainlyest to the first answer. If you need the questions feel free to ask.
ZanzabumX [31]
1.
a. there are 16 nickels so circle 12 
b. 12 times 5=  0.60
2. 
a. 12 dimes
b. there are 12 dimes so circle 10 (1.00)
3. 
a. 10 quarters
b. circle 6 quarters (0.70)
8 0
2 years ago
Read 2 more answers
Find the slope of the line passing through the points (3, 4) and (8,-3).
Verizon [17]

Answer:

-1.4

Step-by-step explanation:

5 0
3 years ago
Alvin is running at a rate of 3 meters per second. The meters he runs, m, in s seconds is given by the equation m=3s. Identify t
dem82 [27]
It is 6 because I got the awnser multiple times
4 0
3 years ago
Read 2 more answers
The yearly attendance at a local movie theater is 82,000 and grows continuously at a rate of 5.1% each year. What is the approxi
juin [17]

Answer:

c. 134,847

Step-by-step explanation:

82,000 x (1.051)^10 = 82,000 x 1.64447456 = 134,847

6 0
3 years ago
Joseph wants to buy a new tennis racquet which cost $200 from the factory. The sports shop marks up the price by 60%. Joseph bou
andriy [413]
Use multipliers:
The normal price the shop would sell the racquet for is:
1.6 * 200 = 320
'1.6' is the multiplier that I got using the percentage. Multiplying a value by 1.6 is the same as increasing the value by 60%. If you multiplied it by 0.1 (which is the same as dividing by 10), you would get just 10% of the value.
Back to the question, now we can use the multiplier 0.75 because we are are reducing the price by 25% (0.25 as a decimal), so:
320 * 0.75 = 240
And now we want just the profit so we take off how much it cost the shop to buy ($200): 240 - 200 = 40
5 0
3 years ago
Other questions:
  • Three minus seventeen= A. Negative B. Positive
    15·2 answers
  • Based on the data, what is the probability that a randomly selected person age 40 or under rated the movie at 4 stars or 5 stars
    14·1 answer
  • On Sunday, 370 people bought tickets to the county fair. Tickets cost $7 for adults and $3 for children. The total revenue from
    14·1 answer
  • You roll a fair six sided die twice. What is the probability of rolling a 3 and then a 5? A) 1 3 B) 1 6 C) 1 12 D) 1 36
    15·2 answers
  • What fraction of a gallon is a quart
    5·2 answers
  • three times the sum of a number x and 3 is 10 plus twice the difference of the number x and another number y
    11·1 answer
  • Pls...Solve n + 8 < - 9
    13·2 answers
  • Rotate AXYZ 270° about the origin, (0,0).
    10·1 answer
  • The graph of the function y = f(x + 26) can be obtained from the graph of
    13·2 answers
  • Find the value of x that makes the equation true.<br><br> 2 = -x
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!