Suppose you toss a coin-You may get a head(H) or tail (T)---2 variations
Suppose you toss it a second time-You may get
HH,HT,TH,TT-4 variations
Suppose you toss once more-
You may get HHH,HHT,HTH,HTT,THH,THT,TTH,TTT-8 variations
Suppose you try to find out the number of cases where 2 heads do not occur in consecutive tosses
You will find the following position-
2 tosses-HT,TH,TT---3 cases
3 tosses-HTH,HTT,THT,TTH,TTT-5 cases
If you procced further you will find the following-
4 tosses-8 cases
5 tosses-13 cases
The number of cases of this occuring are respectively 3,5,8,13....These are numbers in the famous Fibonnaci sequence where each number from the 3rd is the sum of previous 2 numbers
The further number of cases are thus 21,34,55,89,144...etc for 6,7,8,9,10...number of tosses.
Of course the numbers of cases where 2 tails occur in consecutive tosses are also the same.
Suppose you toss it a second time-You may get
HH,HT,TH,TT-4 variations
Suppose you toss once more-
You may get HHH,HHT,HTH,HTT,THH,THT,TTH,TTT-8 variations
Suppose you try to find out the number of cases where 2 heads do not occur in consecutive tosses
You will find the following position-
2 tosses-HT,TH,TT---3 cases
3 tosses-HTH,HTT,THT,TTH,TTT-5 cases
If you procced further you will find the following-
4 tosses-8 cases
5 tosses-13 cases
The number of cases of this occuring are respectively 3,5,8,13....These are numbers in the famous Fibonnaci sequence where each number from the 3rd is the sum of previous 2 numbers
The further number of cases are thus 21,34,55,89,144...etc for 6,7,8,9,10...number of tosses.
Of course the numbers of cases where 2 tails occur in consecutive tosses are also the same.
this is really interesting. a relationship between the binomial distribution and the fibonacci series.
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