Question 364932: This question concerns bit strings of length six. These bit strings can be divided up into four types depending on their initial and terminal bit. Thus the types are: 0XXXX0, 0XXXX1, 1XXXX0, 1XXXX1.
How many bit strings of length six must you select before you are sure to have at least 6 that are of the same type? (Assume that when you select bit strings you always select different ones from ones you have already selected.)
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! you have 4 different types of strings.
call them a, b, c, d
a = 00
b = 01
c = 10
d = 11
since the type of string is determined by the first and last bits only, then the value of the bits in between is irrelevant.
you want to be guaranteed that you will have at least 6 of the same type.
if you draw 5 of each type, then you have drawn 20 strings.
on the next draw, you can be guaranteed that you will have at least 6 of the same type.
that means the minimum number of draws required to guarantee that you have at least 6 of the same type is equal to 21.
|
|
|
