Question 33111: Use a tree diagram showing all possible results when 4 fair coins are tossed. List the ways of getting more than 2 tails.
Answer by longjonsilver(2297)   (Show Source):
You can put this solution on YOUR website! we cannot draw a tree diagram here so i shall have to try to describe it to you:
Start at the left of your page, some way down the page.
Draw 2 diagonal lines showing the 2 outsomes of the 1st coin toss. Label those as H (for Heads) and T (for tails). Against each of those, draw 2 more diagonal lines and lable them H and T twice. Remember to draw the original diagonal lines steep enough because you are going to do this at 4 different positions across the page, each denoting another toss of the coin.
However, you are going to get a lot of repetition down the page because the tree diagram is a representation of ALL the outcomes. Getting a TAIL on the second throw has 2 "origins"...the first toss might have been a HEAD and then the second a TAIL OR first toss was a TAIL and second was also a TAIL.
So, for something with 2 outcomes like a coin toss, we would have 2 outcomes then second event would have 4 (2 sets of 2) and then the third event would have 8 (4 sets of 2) and then the fourth event would have 16 (8 sets of 2).
As i said, i cannot draw it here, but this is the beginning of it, as much as i can do for you:
_____H
__H <
<
__T <
_____T
Now, i know this is a very bad representation...ignore the underscores as they just are there to help me position the < and the H and T.
Along each and every branch, write 0.5 as the probability.
Then read of the tree going left to right, along a set of branches --> one route. Eg following along the top-most branch, we get P(head AND head AND head AND head) = 0.5 * 0.5 * 0.5 * 0.5
P(HHHH) = 1/16
You will find that the probability of every route on this tree is 1/16, since all the probabilities are the same, namely 1/2 for a coin.
You will also see that there are:
1 outcome of HHHH
4 outcomes of HHHT --> HHHT, HHTH, HTHH, THHH
6 outcomes of HHTT
4 outcomes of HTTT
1 outcome of TTTT
And questions will be of the form "find the probability of getting 2 or more heads" or "find the probability of getting more than 1 tail" etc.
More than 2 tails are:
HTTT
THTT
TTHT
TTTH
and
TTTT
jon.
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