document.write( "Question 1091290: the probability of snow tomorrow is 0.6 and the probability that it will be colder is 0.7. the probability that it will not snow and not colder is 0.1. what is the probability that it will snow if it is colder tomorrow?
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Question:
\n" ); document.write( "the probability of snow tomorrow is 0.6 and the probability that it will be colder is 0.7. the probability that it will not snow and not colder is 0.1. what is the probability that it will snow if it is colder tomorrow?
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\n" ); document.write( "Solution:
\n" ); document.write( "Events:
\n" ); document.write( "C=colder; ~C=not colder
\n" ); document.write( "S=snow; ~S=not snow
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\n" ); document.write( "Given
\n" ); document.write( "P(S)=0.6
\n" ); document.write( "P(C)=0.7
\n" ); document.write( "P(~S∩~C)=0.1
\n" ); document.write( "by De Morgan's law
\n" ); document.write( "P(S∪C)=1-P(~S∩~C)=1-0.1=0.9
\n" ); document.write( "=>
\n" ); document.write( "P(S∩C)=P(S)+P(C)-P(S∪C)=0.6+0.7-0.9=0.4
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\n" ); document.write( "P(S|C)=P(S∩C)/P(C)=0.4/0.7=4/7=0.571 (approx.)\r
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