Question

or a 30-day month, 20 days were sunny, 25 days were weekdays, and 18 of the sunny days fell on a weekday. If S is the event that a day is sunny and W is the event that the day is a weekday, find P(S|W) and identify its meaning. anine tenths semicolon the probability that a day is sunny given that it is a weekday beighteen twenty fifths semicolon the probability that a day is sunny given that it is a weekday cnine tenths semicolon the probability that a day is a weekday given that it is sunny deighteen twenty fifths semicolon the probability that a day is a weekday given that it is sunny

Answer 1

$\begin{gathered} p(S)=\frac{20}{30} \\ p(W)=\frac{25}{30} \\ p(S\cap W)=\frac{18}{30} \end{gathered}$

To find

$\begin{gathered} p(S|W)=\frac{p(S\cap W)}{p(W)} \\ \\ p(S|W)=\frac{\frac{18}{30}}{\frac{25}{30}} \\ \\ p(S|W)=\frac{18}{25} \end{gathered}$

Interpretation: eighteen twenty fifths semicolon the probability that a day is sunny given that it is a weekday