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.
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.
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 }
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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