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A commuter must pass through three traffic lights on her
Chapter 4, Problem 15E(choose chapter or problem)
A commuter must pass through three traffic lights on her way to work. For each light, the probability that it is green when she arrives is 0.6. The lights are independent.
a. What is the probability that all three lights are green?
b. The commuter goes to work five days per week. Let \(X\) be the number of times out of the five days in a given week that all three lights are green. Assume the days are independent of one another. What is the distribution of \(X\)?
c. Find P(X = 3).
Equation Transcription:
Text Transcription:
X
Questions & Answers
QUESTION:
A commuter must pass through three traffic lights on her way to work. For each light, the probability that it is green when she arrives is 0.6. The lights are independent.
a. What is the probability that all three lights are green?
b. The commuter goes to work five days per week. Let \(X\) be the number of times out of the five days in a given week that all three lights are green. Assume the days are independent of one another. What is the distribution of \(X\)?
c. Find P(X = 3).
Equation Transcription:
Text Transcription:
X
ANSWER:Solution 15E
Step1 of 4:
Let us consider a computer and it must pass through three traffic lights on her way to work.
P(green) = 0.60 and The lights are independent.
Here X follows binomial distribution with parameters “n and p” that is X B(n, p),
The probability mass function of binomial distribution is given by
, x = 0,1,2,...,n.
Where,
n = sample size
x = random variable
p = probability of success
= 0.60
q = 1 - p (probability of failure)
= 1 - 0.60
= 0.40
Here our goal is:
a).We need to find the probability that all three lights are green.
b).We need to find the distribution of X, when the commuter goes to work five days per week. We have a random variable X it presents the number of times out of the five days in a given week that all three lights are green. Assume the days are independent of one another.