Question

if it rains tomorrow the probability is 0.6 that john will practice his trombone. if it does not rain tomorrow there is only a 0.4 chance that john will practice. suppose the chance of rain tomorrow is 50%what isbthe probability that john will practice his trombone

Answer 1

Let r = rain and p = practice.

Therefore,

`\begin{gathered} Pr\mleft(p\mright)=Pr\mleft(r\mright)* Pr\mleft(p|r\mright)+1-Pr\mleft(r\mright)* Pr\mleft(p|notr\mright) \\ Pr(p)=0.5*0.6\text{ +0.5 x 0.4} \\ =0.3\text{ +0.2} \\ =0.5 \end{gathered}`