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Zillo's picnic

NYSMITH MATHCOUNTS COMMUNITY :: Counting & Probability

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Zillo's picnic Empty Zillo's picnic

Post  Archis Wed Dec 24, 2008 12:53 am

Here's a problem I made to spark the Probability Forum:

Zillian and Zillo live on the planet Zarquon Z. Due to atmospheric pollution, Zarquon Z experiences acidic rainfall with 1/4 of a chance on a SINGLE day. Zillo is planning a picnic for the next five days and hopes for clear skies in that time. What is the probability of NO acidic rainfall the next FIVE days on Zarquon Z?


Last edited by Archis on Thu Mar 26, 2009 4:48 am; edited 1 time in total
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Zillo's picnic Empty Re: Zillo's picnic

Post  Archis Thu Mar 26, 2009 4:47 am

No solutions? The perfect opportunity to drone on about the importance of this problem solving topic:

Complementary probability is key here. Denoted as so:
Zillo's picnic Defaul10

Where, P(A) is defined as a certain probability, the complement is the probability that it will not happen.

The solution to this problem focuses on the fact that (where 1/4 is the probability of Acid Rain and P(A^C) is the probability of no acid rain):
Zillo's picnic Defaul11

The solution asks for the probability that all 5 days have no acid rain or:
Zillo's picnic Defaul12
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NYSMITH MATHCOUNTS COMMUNITY :: Counting & Probability

 
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