<PRE><B>Question 33111</B>
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 &quot;origins&quot;...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 &lt;
&lt;
__T &lt;
_____T


Now, i know this is a very bad representation...ignore the underscores as they just are there to help me position the &lt; 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 --&gt; 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 --&gt; HHHT, HHTH, HTHH, THHH
6 outcomes of HHTT
4 outcomes of HTTT 
1 outcome of TTTT


And questions will be of the form &quot;find the probability of getting 2 or more heads&quot; or &quot;find the probability of getting more than 1 tail&quot; etc.


More than 2 tails are:
HTTT
THTT
TTHT
TTTH


and 


TTTT


jon.
</PRE>