SOLUTION: Please help! Use a tree diagram showing all possible results when four fair coins are tossed. then list the ways of getting exactly two tails.

Question 668552: Please help!

Use a tree diagram showing all possible results when four fair coins are tossed. then list the ways of getting exactly two tails.

Answer by swincher4391(1107) (Show Source): You can put this solution on YOUR website!
Start with your two possibilities {H,T}
From each node in your tree sprout another two branches {H,T} until you've done this process 4 times. As a check, you should have 16 end possibilities. As 2^4 = 16.
Then, find the paths in your tree such that T only appears twice. You should get (from top to bottom:
{HHTT}
{HTHT}
{HTTH}
{THHT}
{THTH}
{TTHH}
6 possibilities.
This makes sense because if we have 4 slots to choose from and we need 2 to be tails, there are exactly (4 choose 2) = 4!/2!*2! = 24/4 = 6 ways to do that.
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