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)}