Earl hates to take out the garbage and to wash the dishes, so he decided 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):

   

   Alternative Method (a):

   		Garbage
   		top edge left$\text{H }0.80$	top edge right$\text{T }0.20$
   Wash	left edge top $\text{H }0.80$	interior top left $\space$ $0.64$ $\space$	interior top right $\space$ $0.16$ $\space$
   	left edge bottom$\text{T }0.20$	interior bottom left blank$\space$ $\space$ $\space$	interior bottom right blank

   Hint (a):

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

   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):

   Use a tree diagram or two-way table.

   Answer (b):

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