Our lives are filled with uncertain events. The terms "luck, chance and probability" are useful in discussing them. When we wish someone "good luck", we are hoping events turn out favorably for them. If someone seems to have events fall their way quite often, we call them "lucky", by which we actually mean "good-lucky". The words "perHAPS", "HAPpiness", "misHAP" and "HAPpenstance" all relate to having good-lucky breaks or their opposite. If I am walking along and the earth cracks open from an earthquake and I fall in, only to have the crack close up and swallow me, that is an unlucky event but is basically one that simply HAPpened. One probabilist used the event of a workman's hammer falling from a repair job on a roof high in the air and killing a passer-by as an example of a similar accident, a mis-HAP.
Sometimes, if we say such an event was "bad luck", we mean the same thing as when we say "it was just chance". Sometimes, the word 'luck' is used to refer to some sort of ongoing personal characteristic or tendency I have or show that is not the same for someone else. A character in the old cartoon "Lil Abner" had a rain cloud that followed him around, always raining on just him and spoiling his days. Such a person has 'bad luck' or even a lack of 'fortune'.
In traditional statistics, statisticians took the chance of 5% to be sufficiently small to more or less ignore. They didn't stick to that standard all the time. If something was especially dangerous, they might advise using the level of 1% instead of the more standard one. The books "Fooled by Randomness" and "The Black Swan" by Taleb, a financial expert, emphasize that low probabilities are not the same as zero chance of something happening. When we say that a fair (whatever that is, it is actually an idea) coin will turn up heads 50% of the time, that 50% is only an average. I can flip it ten times and get 8 heads a bit more than 4% of the time. Those little words "of the time" mean that if I toss a fair coin 10 times over and over, the theory is that a bit more than 4% of those times, I will get 8 heads. I just now tossed a US quarter ten times and got 3 heads. When am I going to get my eight? Who knows?
Real life is more complicated. I may be drunk and have bungled some tosses or lost count. I may be in love and distracted by Her while trying to watch what is happening. I may be feverish or decripit and unable to toss the coin repeatedly without fainting or falling asleep. "The Broken Dice" by Ivar Ekeland tells of two kings rolling dice for possession of an island. The first rolled a 12, which cannot be surpassed with two 6-sided dice. The other tried his luck and rolled a 13! A six on one and the other split in two and resulted in both a 1 and a 6 showing. Not what we expected but what happened. The second king had very good luck.
