[3] Suppose that an airplane has three engines and each of the three engines on airplane functions correctly on a given flight with probability 0.90, and the engines function independently of each other. Assume that the plane can make a safe landing if at least two of its engines are functioning correctly. a) What is the probability that the engines will allow for a safe landing? For the rest of the problem suppose that an airline company has 2 such airplanes (each has three engines and each engine functions properly with prob. 0.90 as in the previous part). Let X be a random variable defined as X = # of airplanes that lands safely out of 2. b) Describe the probability distribution function for the random variable X, i.e., describe the possible values that X can assume and the corresponding probabilities. c) In the next 1000 days, on average how many days the company should expect to hear bad news? (Assume that a crashed airplane is replaced with a new one for the next flight)
[3] Suppose that an airplane has three engines and each of the three engines on airplane functions correctly on a given flight with probability 0.90, and the engines function independently of each other. Assume that the plane can make a safe landing if at least two of its engines are functioning correctly. a) What is the probability that the engines will allow for a safe landing? For the rest of the problem suppose that an airline company has 2 such airplanes (each has three engines and each engine functions properly with prob. 0.90 as in the previous part). Let X be a random variable defined as X = # of airplanes that lands safely out of 2. b) Describe the probability distribution function for the random variable X, i.e., describe the possible values that X can assume and the corresponding probabilities. c) In the next 1000 days, on average how many days the company should expect to hear bad news? (Assume that a crashed airplane is replaced with a new one for the next flight)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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![[3] Suppose that an airplane has three engines and each of the three engines on the
airplane functions correctly on a given flight with probability 0.90, and the engines
function independently of each other. Assume that the plane can make a safe
landing if at least two of its engines are functioning correctly.
a) What is the probability that the engines will allow for a safe landing?
For the rest of the problem suppose that an airline company has 2 such airplanes
(each has three engines and each engine functions properly with prob. 0.90 as in
the previous part). Let X be a random variable defined as
X = # of airplanes that lands safely out of 2.
M
b) Describe the probability distribution function for the random variable X,
i.e., describe the possible values that X can assume and the corresponding
probabilities.
c) In the next 1000 days, on average how many days the company should expect
to hear bad news? (Assume that a crashed airplane is replaced with a new
one for the next flight)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa3574180-5be7-46af-9f18-c1fbb9ec682c%2Fedf17f5c-8bff-4b21-af5d-a884334e7c82%2F0w0jtcf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:[3] Suppose that an airplane has three engines and each of the three engines on the
airplane functions correctly on a given flight with probability 0.90, and the engines
function independently of each other. Assume that the plane can make a safe
landing if at least two of its engines are functioning correctly.
a) What is the probability that the engines will allow for a safe landing?
For the rest of the problem suppose that an airline company has 2 such airplanes
(each has three engines and each engine functions properly with prob. 0.90 as in
the previous part). Let X be a random variable defined as
X = # of airplanes that lands safely out of 2.
M
b) Describe the probability distribution function for the random variable X,
i.e., describe the possible values that X can assume and the corresponding
probabilities.
c) In the next 1000 days, on average how many days the company should expect
to hear bad news? (Assume that a crashed airplane is replaced with a new
one for the next flight)
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