# Zillo's picnic

## Zillo's picnic

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?

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

**Archis**- Admin
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## Re: Zillo's picnic

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

Complementary probability is key here. Denoted as so:

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):

The solution asks for the probability that all 5 days have no acid rain or:

Complementary probability is key here. Denoted as so:

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):

The solution asks for the probability that all 5 days have no acid rain or:

**Archis**- Admin
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Join date : 2008-09-29

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