Get the answers you need from a community of experts on IDNLearn.com. Our Q&A platform offers detailed and trustworthy answers to ensure you have the information you need.
Sagot :
Answer:
0.9606 = 96.06% probability that the system will function tomorrow
Step-by-step explanation:
For each component, there are only two possible outcomes. Either it works, or it does not. Components 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.
Probability of a component working:
0.7 of 0.2(rain)
0.9 of 1 - 0.2 = 0.8(no rain). So
[tex]p = 0.7*0.2 + 0.9*0.8 = 0.86[/tex]
0.86 - 86% probability that the system will function tomorrow
6 components:
This means that [tex]n = 6[/tex]
What is the probability that the system will function tomorrow
This is
[tex]P(X \geq 4) = P(X = 4) + P(X = 5) + P(X = 6)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 4) = C_{6,4}.(0.86)^{4}.(0.14)^{2} = 0.1608[/tex]
[tex]P(X = 5) = C_{6,5}.(0.86)^{5}.(0.14)^{1} = 0.3952[/tex]
[tex]P(X = 6) = C_{6,6}.(0.86)^{6}.(0.14)^{0} = 0.4046[/tex]
[tex]P(X \geq 4) = P(X = 4) + P(X = 5) + P(X = 6) = 0.1608 + 0.3952 + 0.4046 = 0.9606[/tex]
0.9606 = 96.06% probability that the system will function tomorrow
Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. Thank you for choosing IDNLearn.com. We’re dedicated to providing clear answers, so visit us again for more solutions.
