SOLUTION: To harvest all the wheat from a field requires 5 sunny days (although not necessarily consecutive days) and farmer Plough now only has one week left to get the job finished. Given

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Question 1199327: To harvest all the wheat from a field requires 5 sunny days (although not necessarily consecutive days) and farmer Plough now only has one week left to get the job finished. Given that the probability of any day being sunny is 0.8, calculate the probability that he will be able to get the wheat harvested in time.
Answer by ikleyn(52756) About Me  (Show Source):
You can put this solution on YOUR website!
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To harvest all the wheat from a field requires 5 sunny days
(although not necessarily consecutive days) and farmer Plough now only has
one week left to get the job finished. Given that the probability of any day
being sunny is 0.8, calculate the probability that he will be able
to get the wheat harvested in time.
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It is a typical problem on the binomial probability distribution.


The number of trials n= 7; the probability of the success trial is  0.8,  
and the number of success trials k = 5. 


    P = C%5B7%5D%5E5%2A0.8%5E5%2A%281-0.8%29%5E%287-5%29 = %28%287%2A6%29%2F%281%2A2%29%29%2A0.8%5E5%2A0.2%5E2 = 0.27525  (rounded).     ANSWER

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To see many other similar  (and different)  solved problems,  look into the lessons
    - Simple and simplest probability problems on Binomial distribution
    - Typical binomial distribution probability problems
in this site.