SOLUTION: 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

Algebra ->  Probability-and-statistics -> SOLUTION: 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      Log On


   

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?
Answer by mathmate(429) About Me  (Show Source):
You can put this solution on YOUR website!
Question:
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?

Solution:
Events:
C=colder; ~C=not colder
S=snow; ~S=not snow

Given
P(S)=0.6
P(C)=0.7
P(~S∩~C)=0.1
by De Morgan's law
P(S∪C)=1-P(~S∩~C)=1-0.1=0.9
=>
P(S∩C)=P(S)+P(C)-P(S∪C)=0.6+0.7-0.9=0.4

P(S|C)=P(S∩C)/P(C)=0.4/0.7=4/7=0.571 (approx.)