The mind-twisting part of statistics is that Fat Tony is partially right. Because although each independent throw has the probability of one half, the total resulting series is very unlikely.

So you could simultaneously be at awe of the incredible improbability of throwing another heads while proclaiming meh over the 50% chance of the last throw.

It's all a matter of perspective.

Well the answer of 50% is not just mathematically correct, it's simply correct, because the question said we must assume that the coin is fair.

If this was a real life situation, we would assume a reasonable prior for the probability of heads, perhaps with a spike around 0.5 and a small value everywhere else. The posterior would be centered near 1.

The interesting thing is that you can't bias a real coin (unless it's allowed to bounce around after falling). As long as you catch the coin after flipping, you're going to get 50/50 chances, no matter how the coin is weighted. https://www.stat.berkeley.edu/~nolan/Papers/dice.pdf

"Rémy set himself on fire in 2011 in front of a France Télécom office near Bordeaux"

GP doesn't seem to have read the article and is throwing some statistics gimmicks.

I am not saying it was, just that doubling of the rate means little by itself.

If the suicide rate is 17 per 22000, then natural variance alone will push about 14% of random 22k samples into "more than double the base rate" area.

In other words, if you take this indicator alone, then you'll have a false positive about 14% of the time. Obviously, the key word is "alone". With more data about bullying as the cause of suicide you might get better estimations.