Question 243684: Question: Use a tree diagram showing all possible results when four fair coins are tossed. Then list the ways of getting the indicated result of more than two tails.
Hi! I could use a hand, please, on the question above on my homework. I have been working with a tree diagram and I keep getting VERY confused. One coin is easy, when I get to 4 - forget it!
Thank you so very much!!
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Here's one way you can draw a tree diagram. I drew it with a result of 'heads' as each left branch and 'tails' as each right branch.
If we list out the sample space, we get:
{H,H,H,H},
{H,H,H,T},
{H,H,T,H},
{H,H,T,T},
{H,T,H,H},
{H,T,H,T},
{H,T,T,H},
{H,T,T,T},
{T,H,H,H},
{T,H,H,T},
{T,H,T,H},
{T,H,T,T},
{T,T,H,H},
{T,T,H,T},
{T,T,T,H},
{T,T,T,T}
note: if we look at {T,H,T,T} this means that we got tails on the first flip, heads on the second, and then tails on the last two flips.
So the tree is a visual way to represent the sample space. Now let's list all of the elements that have more than two T's. So let's cancel out all of the elements that have two T's, one T or no T's
{H,H,H,H},
{H,H,H,T},
{H,H,T,H},
{H,H,T,T},
{H,T,H,H},
{H,T,H,T},
{H,T,T,H},
{H,T,T,T},
{T,H,H,H},
{T,H,H,T},
{T,H,T,H},
{T,H,T,T},
{T,T,H,H},
{T,T,H,T},
{T,T,T,H},
{T,T,T,T}
what we have left is:
{H,T,T,T},
{T,H,T,T},
{T,T,H,T},
{T,T,T,H},
{T,T,T,T}
Counting them out, we get 5 different ways of getting more than two tails.
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