Salinity in Quebec river is a combination of tides and rain. Rain that diluted the salt occurs about 10% of the time, while the non salty outgoing tides occurs twice per day. You take your dog for a walk down by the river at random during the weekend and notice that he'll drink from the river 30% of the time when the salt is sufficiently low.

A First Course in Probability (10th Edition)
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ISBN:9780134753119
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Chapter1: Combinatorial Analysis
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Salinity in Quebec river is a combination of tides and rain. Rain that diluted the salt occurs about 10% of the time, while the non salty outgoing tides occurs twice per day. You take your dog for a walk down by the river at random during the weekend and notice that he'll drink from the river 30% of the time when the salt is sufficiently low. 

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Given that the overall probability of rain remains 10 % what is the probability of rain during a non tide period? 

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Step 1

From the given information,

Salinity in Quebec river is a combination of tides and rain.

Rain that diluted the salt occurs about 10% of the time, while the non salty outgoing tides occurs twice per day.

The overall probability of rain remains as 10%.

That is,

PRain=10%=0.10PRain|No tide=10%=0.10PRain|tide=0.15Ptide=Pno tide=0.5

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