I was watching a video on Khan Academy about how to compute the probability of getting two heads in a row, given the following:

You have a bag of 8 coins, 5 of which are fair, and 3 of which has a slightly higher chance of getting a head (60% chance). You’ll randomly pick one coin and flip it twice. What’s the probability of getting two heads?

According to Sal (the guy in the video) there’s a 29.125% chance of getting two heads, but I’m not quite convinced, so I wrote some code to simulate the problem.

```
// The numbers represent the chance of getting a head (out of 10)
var headProbs = [
// 5 fair coins
5, 5, 5, 5, 5,
// 3 unfair coins
6, 6, 6
];
var count = 0;
var max = 1e6;
for (var i = 0; i < max; i++) {
// Get a random coin
var rand = Math.floor(Math.random() * 8);
var headProb = headProbs[rand];
// Do two coin flips
// Muliply by 10 so it's easier to compare with the value in `headProb`
// By the way this will produce an integer from 0 to 9.
var flip1 = Math.floor(Math.random() * 10);
var flip2 = Math.floor(Math.random() * 10);
if (flip1 < headProb && flip2 < headProb) {
count++;
}
}
var percent = count / max * 100;
console.log(`Out of ${max} runs, ${count} produced two heads.`);
console.log(`Percentage is ${percent.toFixed(3)}%.`);
console.log('Calculated probability is 29.125%');
```

These are some of the results:

```
Out of 1000000 runs, 291343 produced two heads.
Percentage is 29.134%.
Calculated probability is 29.125%
Out of 1000000 runs, 291363 produced two heads.
Percentage is 29.136%.
Calculated probability is 29.125%
Out of 1000000 runs, 290695 produced two heads.
Percentage is 29.069%.
Calculated probability is 29.125%
```

Assuming my code is correct, I find this convincing. I also find it fun to see that the results produced by simulations match up with calculations