Question 206795
A coin is tossed 6 times. Find the probabilities of getting the following:
a.) Exactly 3 heads
<pre><font size = 4 color = "indigo"><b>
Here is the binomial rule:

If {{{p}}} is the probability of getting {{{1}}} success in {{{1}}} trial,
and {{{n}}} is the number of trials, and {{{q=1-p}}}, then the 
probability of getting exactly {{{r}}} successes out of the {{{n}}} 
trials is

{{{(nCr)(p^r)(q^(n-r))}}}

Here a success will be a head on a coin, and a trial
will be a toss. Here {{{p=1/2}}} is the probability 
of getting {{{1}}} head in {{{1}}} trial. There are {{{6}}}
trials (tosses), so {{{n=6}}}. Then the probability of 
getting exactly {{{3}}} heads out of the {{{6}}} trials 
is gotten by substituting in that expression, with 
{{{q=1-p=1=1/2=1/2}}}.

{{{(6C3)(1/2)^3(1/2)^(6-3)}}}
{{{((6*5*4)/(3*2*1))(1/2)^(3)(1/2)^(3)}}}
{{{(120/6)(1/2)^3(1/2)^3}}}
{{{(20)(1/8)(1/8)}}}
{{{(20)(1/64)}}}
{{{5/16)}}}

Edwin</pre>