SOLUTION: The city water department estimates that for any day in January, the probability of a water main freezing and breaking is 2. For six consecutive days no water mains break. What i

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Question 40007: The city water department estimates that for any day in January, the probability of a water main freezing and breaking is 2. For six consecutive days no water mains break. What is the probability that this will happen?
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Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!
The city water department estimates that for any day in January, the
probability of a water main freezing and breaking is 2.  For six consecutive
days no water mains break.  What is the probability that this will happen?

First of all, no probability of anything could ever be 2.  All probabilities are
between 0 and 1, never 2.  Perhaps you meant .2, not 2.

If the probability that a water main breaks is .2, then the probability that
none break is 1 - .2 = .8.

Assuming water mains breaking are independent events, then we cal multiply their
probabilities.

P(no main breaks the 1st day & no main breaks the 2nd day & no main breaks the
3rd day & no main breaks the 4th day & no main breaks the 5th day & no main
breaks the 6th day) =  

P(no main breaks the 1st day) × P(no main breaks the 2nd day) × P(no main
breaks the 3rd day) × P(no main breaks the 4th day) × P(no main breaks the 5th
day) × P(no main breaks the 6th day) = 

(.8)(.8)(.8)(.8)(.8)(.8) = (.8)6 = .262144

Edwin