SOLUTION: 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)?

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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)?
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
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)? 
That's a binomial probability problem.

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

(1)  By formula

 





.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
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