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{Birthday Probability}

The Question

How many students need to be in a class such that at least two students share the same birthday?

For birthday, we mean day of the year e.g. March 4th

Approach

• We can use Monte Carlo simulation to determine the answer
• Monte Carlo simulation works by repeatedly sampling to obtain numerical results
• For each sample we generate random birthdays (i.e. numbers between 0 and 364) until two birthdays are the same
• The number of birthdays we generate in each sample equals the number of students in the class for that sample
• We repeat each sample X number of times and then determine the average number of birthdays over all samples

function birthdayProbability(numSimulations){
    var numStudents = 0;
    
    for(let i = 0; i < numSimulations; i++){
        let studentsBday = [];
        
        do{
            studentsBday.push(Math.round(Math.random()*364));
            var index = studentsBday.indexOf(studentsBday[studentsBday.length - 1]);
        }while(index === studentsBday.length - 1)
        
        numStudents += studentsBday.length;
    }
    
    return Math.ceil(numStudents / numSimulations);
}

birthdayProbability(10000); 
//we can repeat the simulations until the solution is stable
//here we arbitrarily select a sample size of 10,000

Solution

Solution