Reference no: EM132847023
1) Suppose a sample space has things a,b,and c. Twice draw from the sample space and replace. The possible sequences formed are aa,ac,ba,bb,bc, ca,cc).
Now suppose there are Y different things. There are Y ways the first draw can occur. For each of the Y ways the first draw can occur, there are Y ways the second draw can occur, resulting in Y times Y. Or Y^2 sequences. For each of the Y^2 sequences formed from two draws , there are Y ways the third draw can occur forming Y^3 sequences. Generalizing there are Y^x sequences formed by drawing X times from Y different things with replacement,
Example The number of state license plate that can be made with 3 letters followed by 3 numbers is 26 x 26 x 26 x 10x 10x 10=26^3 x 20^3= 17.576.000. From this one style of plate , there are many sequences.
How many sequences of 3 things can be formed from 9 different things with replacement and order us important.?
2. If you toss a dice twice , what is the sample space if you want to restrict the results to only the outcomes where adding the the results of the throws together equals seven?. For example, if you get 1 on the first toss and 6 on the second toss, these two tosses meet the criteria.
A) S= {7}
b) S=(1,6),(2,5),(3,4),
c) S= { (1,6),(2,5),(3,4),(4,3),(5,2),(6,1)}
d) S= {(1,6), (2,5), ( 3,4)
e) S ={ 2,5),(5,2),(1,6), (6,1)}
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