Earl hates taking out the garbage and he hates washing the dishes, so he decides to make a deal with his parents: He will flip a coin once for each chore and will perform the chore if the coin lands on heads. What he doesn’t know is that his parents are going to use a weighted coin that lands on heads $80\%$ of the time!

1. What is the probability that Earl will have to do both chores?

   Step 1(a):

   

   Hint (a):

   What is the probability of flipping two heads in a row?

   Alternative Method (a):

   Garbage
   Wash		$\color{green}{\text{H }0.80}$	$\color{green}{\text{T }0.20}$
   	$\color{green}{\text{H }0.80}$	$\color{green}{0.64}$	$\color{green}{0.16}$
   	$\color{green}{\text{T }0.20}$

   Answer (a):

   $(0.80)(0.80)=0.64=64\%$

2. What is the probability that Earl will have to take out the garbage but will not need to wash the dishes?

   Hint (b):

   This is Heads for garbage and Tails for wash in your diagram.

   Answer (b):

   $(0.80)(0.20)=0.16=16\%$