HOW TO FIND SAMPLE SPACE FOR TOSSING OF FIVE COINS

Let us discuss the coin toss probability formula, sample space of tossing 1 coin , sample space of tossing 2 coins , sample space of tossing 5 coins , How to make a tree diagram.

To find the sample space for tossing of one  coin

we know that there are two outcomes in tossing of coin . Out of two outcome one is H and second is T.
So  Put H and T in sample space 'S'
S = {H , T}

To find the sample space for tossing of two coins

1st put  2²   = 4  elements in a set of sample space,

1st character of 1st two elements must be H and 1st character of last two elements must be T .

2nd character of all the  elements must be H and T alternatively

 ^{S={ HH , HT , TH , TT}}

To find the sample space for tossing of three coins

1    Put  2³  = 8  elements in a set of sample space,
2    1st character of 1st four elements must be H and 1st character of last four elements must be T .

3   2nd character of 1st ,2nd ,5th and 6th  elements must be H and  2nd character of 3rd, 4th, 7th and 8th  elements must be T alternatively

4    Last character of all the  elements must be H and T alternatively.

Therefore sample  space  'S'  is given by

S = { HHH , HHT , HTH , HTT ,THH, THT , TTH , TTT }

To find the sample space for tossing of Four coins

1    Put  2⁴  = 16  elements in a set ,
2    1st character of 1st eight elements must be H and 1st character of last eight elements must be T.

3   2nd character of 1st four and 9th to 12th  elements must be H and  2nd character of 5th, 6th , 7th and 8th and last four elements must be T alternatively.

4  3rd character for 1st , 2nd , 5th , 6th , 9th , 10th , 13th and 14th elements must be H and for remaining characters ( 3rd , 4th ,7th ,8th , 11th ,12th ,15th and 16th)  it must be T.

5    Last character of all the  elements must be H and T alternatively.

Hence sample space ' S' is given by 

S = { HHHH , HHHT , HHTH , HHTT , HTHH , HTHT , HTTH , HTTT , THHH , THHT , THTH , THTT , TTHH , TTHT , TTTH , TTTT }

To find the sample space for tossing of Five Coins

1    Put  2⁵  = 32  elements in a set ,
2    1st character of 1st sixteen elements must be H and 1st character of last sixteen elements must be T.

3   2nd character of 1st eight and  17th to 24th  elements must be H and  2nd character of 9th to 16th and 25th to 32nd  elements must be T alternatively.

4  3rd character for 1st four , 9th to 12th , 17th to 20th , 25th to 28th elements must be H , And  3rd character for 5th to 8th , 13th to 16th , 21st to 24th and 29th to 32nd elements  must be T.

5  4th character for 1st two ,5th and 6th ,9th and 10th , 13th and 14th , 17th and 18th, 21st and 22nd , 25th and 26th, 29th and 30th and 32nd must be H  And 3rd and 4th , 7th and 8th , 11th and 12th and 15th and 16th , 19th and 20th , 23rd and 24th , 27th and 28th , 31st and 32nd elements must be T.

6    Last character of all the  elements must be H and T alternatively.

Hence sample space ' S' is given by 


S = { HHHHH , HHHHT , HHHTH , HHHTT , HHTHH , HHTHT , HHTTH , HHTTT , HTHHH, HTHHT, HTHTH , HTHTT, HTTHH, HTTHT, HTTTH, HTTTT, THHHH , THHHT , THHTH , THHTT , THTHH , THTHT , THTTH , THTTT ,TTHHH , TTHHT, TTHTH , TTHTT, TTTHH, TTTHT , TTTTH , TTTTT }

^{Watch this video for finding sample space of coins}

Final Words

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