Question 643440
>>Martin beats Jelena in 2 games out of 3 at tennis.<< 
<pre>
Therefore Jelena wins only 1 game out of 3 when playing agains Martin.

Therefore Jelena's probability of winning against Martin is {{{1/3}}}</pre>>>What is the probability that jelena wins a set of tennis 6 games to 4?<<
<pre>
That's asking what is the probability that Jelena, playing aginst Martin,
will win 6 times and lose 4 times.  That means she plays a total of 6+4 or
10 games and wins 6 out of the 10 games.  [That's not very likely to happen,
since she usually loses to Martin, so we expect a very low probability]

That's the binomial probability of succeeding x=6 times out of n=10 trials,
with a probability of p={{{1/3}}}.

The binomial probability of succeeding x times out of n trials, with a
probability of p is given by the formula:

          C(n,x)·p<sup>x</sup>·(1-p)<sup>n-x</sup>

Substituting

          C(10,6)·{{{(1/3)}}}<sup>6</sup>·(1-{{{1/3}}})<sup>10-6</sup>

          C(10,6)·{{{(1/3)}}}<sup>6</sup>·(1-{{{1/3}}})<sup>10-6</sup>

          210·{{{1/729}}}·{{{(2/3)}}}<sup>4</sup>

          210·{{{1/729}}}·{{{16/81}}}

          {{{3360/59049}}}

          {{{1120/19683}}}

As a decimal 0.056901895  (round off as you were told).

You can also do it with a TI-83 or TI-84. You may have the
older model or the newer model.  Either way,

Press 2ND VARS ALPHA MATH 

-------------------------------------
If you have an older model press ENTER

You will see

binompdf(

Make it read

binompdf(10,1/3,
6)

press ENTER

you will see .056901895
-------------------------------------
If you have a newer model, you will see 

trials: 
p:
x value:
Paste 

Make it read this way:

trials: 10 
p:1/3
x value:6
Paste 

Highlight Paste then press ENTER

You will see

binompdf(10,1/3,
6)

press ENTER

you will see .056901895


Edwin</pre>