## 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 2

^{2 }= 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 2

^{3 }= 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 2

2 1st character of 1st

^{4 }= 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 }

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 2^{5 }= 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 }**##
^{}^{Watch this video for finding sample space of coins}

^{}

## Final Words

Thanks for giving your precious time to read this post regarding probability formula, sample space of tossing 1 coin , sample space of tossing 5 coins , How to make a tree diagram.. If you liked it then share it with your near and dear ones to benefit them. we shall meet in next post with another beneficial article till then bye ,take care.......

If you are a mathematician Don't forget to visit my Mathematics You tube channel ,Mathematics Website and Mathematics Facebook Page , whose links are given below

## No comments:

## Post a Comment