Question

If it is snowing, there is an 80% chance that class will be canceled. If it is not snowing, there is a 95% chance that class will go on. Generally, there is a 5% chance that it snows in NJ in the winter. If we are having class today, what is the chance that it is snowing?

Answer 1

`P(S|\bar{C} ) = 0.1739`

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

`P( \bar{C} | \bar{S}) = 0.95`

and P(S) = 0.05

We need calculate

`P( S |\bar{C} ) = \frac{P(\bar{C} | S) P(S)}{P(\bar{C})}`

`P(\bar{C}) = P( \bar{C}|S)P(S) + P( \bar{C}|\bar{S})P(\bar{S})`

How

`P(C | S) = 0.8` then
`P( \bar{C} | S) = 0.2`

`P (\bar{C})` = (0.2)(0.5) + (0.95)(0.5)

=0.575

`P(S |\bar{C} ) = ((0.2)(0.5))/((0.575))`

`P(S|\bar{C} ) = 0.1739`