Question 1042673: Solar power plants in the Mojave desert in Cali use over 900,000 mirrors to ceoncentrate the sun's rays and generate about 350 MW of electric power using steam turbines. Random wind gusts cause 8 mirrors to break per 24-hour day on average.
a) A mirror has just been broken. What is the probability that the next mirror will break sometime during the next 5 hours?
b) A mirror has just been broken. What is the probability that the next mirror will break exactly 5 hours from now?
c)A mirror has just been broken. What is the probability that exactly 3 mirrors will break during the next 5 hours?
d) The last mirror broke 2 hours ago. What is the probability the next mirror will break sometime during the next 3 hours?
If someone can help me solve this, THANK YOU SO MUCH in advance !!!!
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! This is a binomial (break/don't break) with very small probability of breakage and a very large sample with a constant probability of n*p=8 per 24 hours or 8*(5/24)=5/3 per 5 hours. That is lambda.
P=e-(lambda)*lambda^x/x!, where x is the number of breakages here.
e^(-5/3)*5/3^1/1!
=0.3148 probability of breaking in next 5 hours.
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To me, exactly 5 hours from now is an infinitely small point and therefore an infinitely small probability.
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For 3 mirrors,
e^(-3)^(5/3)^3/3!
=0.0384
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Over a small interval, the probability of an occurrence is approximately proportional to the size of the interval. The probability of an event in a certain interval does not change over different intervals.
I would say the probability is 3/5 of the probability in the next 5 hours or 0.1889.
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