# Probability of getting at least K heads in N tosses of Coins in C++

C++Server Side ProgrammingProgramming

Probability is the chances of getting the desired output from the set of data available. The range of probability lie between 0 and 1 where an integer 0 shows the chances of impossibility and 1 indicates certainty.

What is probability?

Probability in mathematics gives us the tools that tell the uncertainty of the events and reasons. In other words we can say probability deals with calculating the likelihood of a given event’s occurrence, which can be expressed as a number between 1 and 0. For example: the probability of getting a head’s when an unbiased coin is tossed, or getting a 3 when a dice is rolled.

Now, coming back to the question we have to find the probability of getting at least k heads in N tosses of coins.

Like we have 3 coins and k as 2 so there are23= 8 ways to toss the coins that is −

HHH, HTH, HHT, HTT, THH, THT, TTT, TTH.

And the sets which contains at least 2 heads are −

HHH, HTH, HHT, THH.

So the probability will be 4/8 or 0.5.

## Example

Input: k = 1, n = 3
Output: 0.875

Input: k = 3, n = 6
Output: 0.65625

Approach we will be following to solve the above problem −

• We will take n and k as an input.
• Store the value of factorial in an array and call it whenever it is required.
• Perform the calculation.
• Return the result.

## Algorithm

Step 1-> declare function to calculate the probability of getting at least k heads in n tosses
double probability(int k, int n)
Declare and set double check = 0
Loop For i = k and i <= n and ++i
Set check += temp[n] / (temp[i] * temp[n - i])
End
Call check = check / (1LL << n)
return check
Step 2-> declare function to precompute the value
void precompute()
Set temp = temp = 1
Loop For i = 2 and i < 20 and ++i
Set temp[i] = temp[i - 1] * i
Step 3-> In main
Call precompute()
Call probability(1, 3)
Stop

## Example

Live Demo

#include<bits/stdc++.h>
using namespace std;
#define size 21
double temp[size];
// calculate probability of getting at least k heads in n tosses.
double probability(int k, int n) {
double check = 0;
for (int i = k; i <= n; ++i)
check += temp[n] / (temp[i] * temp[n - i]);
check = check / (1LL << n);
return check;
}
void precompute() {
temp = temp = 1;
for (int i = 2; i < 20; ++i)
temp[i] = temp[i - 1] * i;
}
int main() {
precompute();
// Probability of getting 1 head out of 3 coins
cout<<"probability is : "<<probability(1, 3) << "\n";
// Probability of getting 3 head out of 6 coins
cout<<"probability is : "<<probability(3, 6) <<"\n";
return 0;
}

## Output

probability is : 0.875
probability is : 0.65625