Answer:
[tex]P(S|\bar{C} ) = 0.1739[/tex]
Step-by-step explanation:
We define the probabilistic events how:
S: Today is snowing
C: The class is canceled
If it is snowing, there is an 80% chance that class will be canceled, it means
P( C | S ) = 0.8 conditional probability
If it is not snowing, there is a 95% chance that class will go on
[tex]P( \bar{C} | \bar{S}) = 0.95[/tex]
and P(S) = 0.05
We need calculate
[tex]P( S |\bar{C} ) = \frac{P(\bar{C} | S) P(S)}{P(\bar{C})}[/tex]
[tex]P(\bar{C}) = P( \bar{C}|S)P(S) + P( \bar{C}|\bar{S})P(\bar{S})[/tex]
How
[tex]P(C | S) = 0.8[/tex] then [tex]P( \bar{C} | S) = 0.2[/tex]
[tex]P (\bar{C})[/tex] = (0.2)(0.5) + (0.95)(0.5)
=0.575
[tex]P(S |\bar{C} ) = \frac{(0.2)(0.5)}{(0.575)}[/tex]
[tex]P(S|\bar{C} ) = 0.1739[/tex]
