Question 499325
A fair die is rolled 10 times. What is the probability that an odd number (1, 3 or 5) will occur between 2 and 4 times (inclusive)? 
<pre>
That's a binomial probability problem.

There are three ways, (1) By formula, (2) By table, (3) By TI-84 calculator

(1)  By formula

{{{sum((  matrix(1,1,"C(n,x)"*p^n*q^(n-x) ) ),x=2,4)}}}{{{""=""}}}{{{sum((  matrix(1,1,"C(10,x)"*(1/2)^x*(1/2)^(10-x) ) ),x=2,4)}}}{{{""=""}}}{{{"C(10,2)"*(1/2)^2*(1/2)^(10-2)+"C(10,3)"*(1/2)^3*(1/2)^(10-3)+"C(10,4)"*(1/2)^4*(1/2)^(10-4)}}}{{{""=""}}} 

{{{"C(10,2)"*(1/2)^2*(1/2)^8+"C(10,3)"*(1/2)^3*(1/2)^7+"C(10,4)"*(1/2)^4*(1/2)^6}}}{{{""=""}}}{{{"C(10,2)"*(1/2)^10+"C(10,3)"*(1/2)^10+"C(10,4)"*(1/2)^10}}}{{{""=""}}}

{{{( "C(10,2)"+"C(10,3)"+"C(10,4)" )*(1/2)^10}}}

{{{( (10*9)/(2*1)+(10*9*8)/(3*2*1)+(10*9*8*7)/(4*3*2*1))*(1/2)^10}}}{{{""=""}}}{{{(45+120+210)*(1/2^10)}}}{{{""=""}}}{{{375/1024}}}{{{""=""}}}.3662109375

(2) By table.   There are two kinds of binomial tables, cumulative and
non-cumulative.

Go to the binomial table for n=10, find the row for x (or r on some tables)
as 4 and go across to the column headed .5 or .50.

A.  If your table is cumulative, then you will read .3770.

    1. find the row for x=2 and go across to the column headed .5 or .50, and
read .0107

    2. Subtract .3770-.0107 = .3663

B.  If your table is not cumulative, you will read .2051. 

    1. find the row for x=3 and go across to the column headed .5 or .50, and
read .1172
    2. find the row for x=2 and go across to the column headed .5 or .50, and
read .0439
    3. Add .2051+.1172+.0439 and get .3662.

(3) By TI-84 calculator

Press 2nd
Press VARS ALPHA APPS

If you have older version, you will see

binomcdf(10,.5,4
)

If you have the newer version you have to first answer 
trials:10, p:.5, x value: 4, highlight and click Paste

Press ENTER

Press —  (minus)

Press 2nd
Press VARS ALPHA APPS

If you have older version, you will see

binomcdf(10,.5,4
)-binomcdf(10,.5
,1)

If you have the newer version you first have to answer 
trials:10, p:.5, x value: 1, highlight and click Paste

Press ENTER


Read .3662109375

Edwin</pre>