42 lines
1.4 KiB
Python
42 lines
1.4 KiB
Python
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import random
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# Problem:
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# 2.11
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# At a completely random moment between 6:30 and 7:30 a.m.,
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# the morning newspaper is delivered to Mr. Johnson’s residence.
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# Mr. Johnson leaves for work at a completely random moment
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# between 7:00 and 8:00 a.m. regardless of whether the newspaper
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# has been delivered. What is the probability that Mr. Johnson can
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# take the newspaper with him to work? Use computer simulation to
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# find the probability.
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#
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# Solution:
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# Applying Bayes' theorem.
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# Newsletter arrives in interval 6:30 - 7:00 ?
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# yes| p=0.5 no| p=0.5
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# | Mr. Jonhnson leaves in interval 7:00 - 7:30
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# | yes| p=0.5 no| p=0.5
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# | Newsletter arrives first in |
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# | interval 7:00-7:30 |
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# | yes| p=0.5 no| p=0.5 |
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# | | |
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# 0.5 + 0.5*0.5*0.5 + 0.5*0.5 = 0.875
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#
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# Simulation:
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# 0.874867
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# 0.874876
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# 0.874876
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#
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newspaper_arrived_on_time = 0
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samples = 10000000
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for i in range(samples):
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n = random.random()
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w = random.random() + 0.5
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if w >= n:
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newspaper_arrived_on_time += 1
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print('simulated probability of ontime arrived newspaper is : {}'
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.format(newspaper_arrived_on_time/samples))
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