Flip 100000 Coins

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Flip coin(s) times

Features of this Coin Tosser

  • Toss a coin
  • Uses American dime for the toss
  • Also allows side landing according to the probability of 1 in 6000
  • Start and Stop the coin at your own will

Statistics of this Coin Flipper

  • Flip 100000 Coins
    Total Possible Combinations INF

    Number of combinations are calculated using the formula
    [ (2+100000-1) choose (100000) ] or [ 100001 choose 100000 ]
    where 2 is the number of sides of the coin and 100000 is the number of coins.

    You can try generating all the combinations of Heads and Tails using the following combination generator
    All possible combinations of 100000 coins
  • Flip 100000 Coins
    Total Possible Permutations INF

    Number of permutations are calculated using the formula [ 2^100000 ]
    where 2 is the number of sides of the coin and 100000 is the number of coins.

    You can try generating all the permutations of Heads and Tails using the following permutations generator
    All possible permutations of 100000 coins

Probabilities of this 100000 Coin Tosser

Assuming that all the coins are fair coins and probability of getting either Heads or Tails is 1/2 or 50%

Probability of getting a Heads when flipping a coin 100000 times

In technical terms, this is equivalent of getting atleast one Heads.

Probability of getting atleast one Heads is close to 1., about 100% percent.

The probability of getting atleast one Heads is calculated by multiplying all the probabilities of not getting a Heads for each coin and then subtracting the answer from 1.

P(Heads>=1)
            = 1 - [ P(H=0)Coin1 x P(H=0)Coin2 x P(H=0)Coin3 x P(H=0)Coin4 x P(H=0)Coin5 x P(H=0)Coin6 x P(H=0)Coin7 x P(H=0)Coin8 x P(H=0)Coin9 x P(H=0)Coin10 x P(H=0)Coin11 x P(H=0)Coin12 x P(H=0)Coin13 x P(H=0)Coin14 x P(H=0)Coin15 x P(H=0)Coin16 x P(H=0)Coin17 x P(H=0)Coin18 x P(H=0)Coin19 x P(H=0)Coin20 x ... ]
            = 1 - [ 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x ... ]
            
You can generate all possible permutations and combinations of 100000 Coins containing atleast one Heads using the following permutations and combinations generator All possible combinations of 100000 coins with atleast one Heads All possible permutations of 100000 coins with atleast one Heads

To verify the answer, you can divide the number of permutations containing atleast 1 Heads by number of total possible permutations of 100000 coins.

Probability of not getting a Heads when flipping 100000 Coins

Probability of not getting any Heads is close to 0., about 0.% percent.

Probability of getting zero Heads is calculated by multiplying all the probabilities of not getting a Heads for each coin.

P(Heads=0)
            = P(H=0)Coin1 x P(H=0)Coin2 x P(H=0)Coin3 x P(H=0)Coin4 x P(H=0)Coin5 x P(H=0)Coin6 x P(H=0)Coin7 x P(H=0)Coin8 x P(H=0)Coin9 x P(H=0)Coin10 x P(H=0)Coin11 x P(H=0)Coin12 x P(H=0)Coin13 x P(H=0)Coin14 x P(H=0)Coin15 x P(H=0)Coin16 x P(H=0)Coin17 x P(H=0)Coin18 x P(H=0)Coin19 x P(H=0)Coin20 x ...
            = 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x ...            

Probability of getting exactly 1 Heads or 99999 Tails when flipping 100000 Coins

Probability of getting exactly 1 Heads is close to 0., about 0.% percent.

You can calculate this using counting or by using the binomial distribution

Using Counting

You can think of 100000 coins as spots to be filled. There are INF ways to fill these spots with either a Heads or Tails (all possible permutations). Now, we need to find how many of these permutations contain exactly 1 Heads. In other words, in how many different ways can we place 1 Heads in 100000 spots? Or, in how many ways can we pick 1 out of 100000 spots? The answer can be caclulated using the formula [ 100000 choose 1 ]. So, there are 100000 ways to choose 1 out of 100000 spots. The probability is calculated by dividing the number of ways to pick 1 spots by the number of total permuations.

P (H=1)
                = Ways to pick 1 out of 100000 spots / Total permutations of 100000 coins
                = (100000 choose 1) / (2^100000)                
                = 100000 / INF                

Using Binomial Distribution

In Binomial Distribution, we look for k number of successful events in n number of trials where p is the probability of each successful event. Here, a successful event means getting a Heads and an event means a coin flip.

To get exactly 1 Heads, we need k=1 successful events out of total n=100000 events. Each event has a probability p=1/2 of occuring.

Probability of k=1 successful events is then calculated as follows.
P(k=1)
                = (n choose k) pk (1-p)n-k
                = (100000 choose 1) (1/2)1 (1/2)100000-1
                = (100000 choose 1) (1/2)100000
                = 100000 x (1/INF)
                

You can generate all possible permutations and combinations of 100000 Coins containing exactly 1 Heads using the following permutations and combinations generator All possible combinations of 100000 coins with exactly 1 Heads All possible permutations of 100000 coins with exactly 1 Heads

To verify the answer, you can divide the number of permutations containing exactly 1 Heads by number of total possible permutations.

Probability of getting exactly 50000 Heads or 50000 Tails when flipping 100000 Coins

Probability of getting exactly 50000 Heads is close to NaN, about NAN% percent.

You can calculate this using counting or by using the binomial distribution

Using Counting

You can think of 100000 coins as spots to be filled. There are INF ways to fill these spots with either a Heads or Tails (all possible permutations). Now, we need to find how many of these permutations contain exactly 50000 Heads. In other words, in how many different ways can we place 50000 Heads in 100000 spots? Or, in how many ways can we pick 50000 out of 100000 spots? The answer can be caclulated using the formula [ 100000 choose 50000 ]. So, there are INF ways to choose 50000 out of 100000 spots. The probability is calculated by dividing the number of ways to pick 50000 spots by the number of total permuations.

P (H=50000)
                = Ways to pick 50000 out of 100000 spots / Total permutations of 100000 coins
                = (100000 choose 50000) / (2^100000)                
                = INF / INF                

Using Binomial Distribution

In Binomial Distribution, we look for k number of successful events in n number of trials where p is the probability of each successful event. Here, a successful event means getting a Heads and an event means a coin flip.

To get exactly 50000 Heads, we need k=50000 successful events out of total n=100000 events. Each event has a probability p=1/2 of occuring.

Probability of k=50000 successful events is then calculated as follows.
P(k=50000)
                = (n choose k) pk (1-p)n-k
                = (100000 choose 50000) (1/2)50000 (1/2)100000-50000
                = (100000 choose 50000) (1/2)100000
                = INF x (1/INF)
                

You can generate all possible permutations and combinations of 100000 Coins containing exactly 50000 Heads using the following permutations and combinations generator All possible combinations of 100000 coins with exactly 50000 Heads All possible permutations of 100000 coins with exactly 50000 Heads

To verify the answer, you can divide the number of permutations containing exactly 50000 Heads by number of total possible permutations.

Probability of getting exactly 99999 Heads or 1 Tails when flipping 100000 Coins

Probability of getting exactly 99999 Heads is close to NaN, about NAN% percent.

You can calculate this using counting or by using the binomial distribution

Using Counting

You can think of 100000 coins as spots to be filled. There are INF ways to fill these spots with either a Heads or Tails (all possible permutations). Now, we need to find how many of these permutations contain exactly 99999 Heads. In other words, in how many different ways can we place 99999 Heads in 100000 spots? Or, in how many ways can we pick 99999 out of 100000 spots? The answer can be caclulated using the formula [ 100000 choose 99999 ]. So, there are INF ways to choose 99999 out of 100000 spots. The probability is calculated by dividing the number of ways to pick 99999 spots by the number of total permuations.

P (H=99999)
                = Ways to pick 99999 out of 100000 spots / Total permutations of 100000 coins
                = (100000 choose 99999) / (2^100000)                
                = INF / INF                

Using Binomial Distribution

In Binomial Distribution, we look for k number of successful events in n number of trials where p is the probability of each successful event. Here, a successful event means getting a Heads and an event means a coin flip.

To get exactly 99999 Heads, we need k=99999 successful events out of total n=100000 events. Each event has a probability p=1/2 of occuring.

Probability of k=99999 successful events is then calculated as follows.
P(k=99999)
                = (n choose k) pk (1-p)n-k
                = (100000 choose 99999) (1/2)99999 (1/2)100000-99999
                = (100000 choose 99999) (1/2)100000
                = INF x (1/INF)
                

You can generate all possible permutations and combinations of 100000 Coins containing exactly 99999 Heads using the following permutations and combinations generator All possible combinations of 100000 coins with exactly 99999 Heads All possible permutations of 100000 coins with exactly 99999 Heads

To verify the answer, you can divide the number of permutations containing exactly 99999 Heads by number of total possible permutations.

Probability of getting all Heads when flipping 100000 Coins

Probability of getting all Heads is close to 0., about 0.% percent.

This is calculated by multiplying together all the probabilities of getting a Heads for each coin.

P(Heads=100000)
            = P(H=1)Coin1 x P(H=1)Coin2 x P(H=1)Coin3 x P(H=1)Coin4 x P(H=1)Coin5 x P(H=1)Coin6 x P(H=1)Coin7 x P(H=1)Coin8 x P(H=1)Coin9 x P(H=1)Coin10 x P(H=1)Coin11 x P(H=1)Coin12 x P(H=1)Coin13 x P(H=1)Coin14 x P(H=1)Coin15 x P(H=1)Coin16 x P(H=1)Coin17 x P(H=1)Coin18 x P(H=1)Coin19 x P(H=1)Coin20 x ...
            = 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x ...            

Probability of getting one of a kind when flipping 100000 Coins

Probability of getting one of a kind is close to 0., about 0.% percent.

There are 2 ways to get one of a kind (all Heads or all Tails). The probability of getting all of any kind is then caclulated by adding the probability of getting all Heads or all Tails. Since, probabilities of getting all Heads or all Tails are the same, we can just multiply one of them by 2. So, multiplying the probability of getting all Heads by 2 will give us the probability of getting all of any kind.

 
    Probability of getting all of a kind
        = Pobability of getting all Heads + Pobability of getting all Tails 
        = 2 x Pobability of getting all Heads
        = 2 x (1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x ...)    
    

Javascript code to Flip 100000 Coins


    // Flip 100000 Coins
    
                   
        // define the range of numbers to pick from
        var lowest = 1;             // lowest possible side of the coin // 1 for heads
        var highest = 2;           // highest possible side of the coin // 2 for tails
        var number_of_coins = 100000;    // how many coins to flip     

        // allow the coin to land on the side 
        // change to false if sidelanding not desired
        var allow_sidelanding = true; 

        var PROBABILITY_OF_SIDELANDING = 6000; // set the probability of sidelanding to 1 in 6000
        
        var this_flip = []; // array to store the results of this flip

        for (var j = 1; j <= number_of_coins; j++) {

            // loop for the number of coins

            // for each coin, generate a number between lowest and highest i.e. 1 or 2
            var coin_face = Math.floor(Math.random() * (highest-lowest+1) + lowest);

            // if sidelanding is allowed
            if (allow_sidelanding) {

                // first check for sidelanding scenario with given probability
                var edge = Math.floor(Math.random() * (PROBABILITY_OF_SIDELANDING-1+1) + 1);

                // if sidelanding is probable, override the coin face with edge value i.e. 3
                // i.e. if we generated a 1 when generating a number between 1 and PROBABILITY_OF_SIDELANDING
                if (edge === 1) {
                    coin_face = 3;
                }

            }


            this_flip.push(coin_face); //store this in the array
        }
            
        
        // print all the generated flips
            
        for (j = 0; j < this_flip.length; j++) {

            // loop through the coin array 

            //print each coin flip value followed by a space
            document.write(this_flip[j]);
            document.write(" ");

        }
            
        
    

    /* 

    Sample output 

    

    */
    


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