### Instruction: Sheila has been invited to a picnic tomorrow.  The picnic will occur, rain or shine.  If it rains, there is a $20\%$ probability that Sheila will decide to go, but if it is sunny, there is an $80\%$ probability that Sheila will decide to go.  The forecast for tomorrow states that there is a $40\%$ chance of rain.  What is the probability that Sheila will attend the picnic? Express your answer as a percent.### Response: So there is a $40\%$ chance of rain and a $60\%$ chance of sun.
And if it rains, there is a $20\%$ chance that Sheila will go, but if it's sunny, there is an $80\%$ chance that Sheila will go.
So the probability that Sheila will go is $40\% \cdot 20\% + 60\% \cdot 80\%$.
That's $8\% + 48\%$ which is $56\%$.