Someone says “you have 1 out of 370 chances to win a bottle of water”
and you win 2 consecutive times in a row, what does that mean? i’m lucky or the probability is wrong?
In: Mathematics
There’s a *theoretical probability* – this is where you look at the possible outcomes of an event and decide what the odds of each outcome are. An easy example is a coin flip – it has two sides. On a flip of the coin, you have a 1 in 2 chance of getting one side or the other (50% chance). Or a die, with six sides. When you toss the die, you have a 1 in 6 chance of getting any one side.
Then there’s the actual or observed probability. This is based off of how many “events” or trials you actually run. So, if you flip a coin 10 times, you are actually likely *not* to get 5 Tails and 5 Heads, but maybe 6/4 or 7/3. Out of this real set of 10 trials, your observed probability of getting Tails might therefore be 60% or 70%.
*But*, the more trials you run, the closer to the *theoretical* probability you get. It’s called the *Law of Large Numbers*. So if you flip the coin 100 times, you might get Tails 55% of the time. Flip it 1000 times and you might get Tails 50.2% of the time.
Long story short, in your example, the person got lucky if they won twice in a row. Someone else playing this game could maybe go 800 times without winning once. But the longer the game goes on, the closer you’ll see the math work out to “1 in 370”.
edit: When they say “1 in 370 odds”, it could very well be that first theoretical probability. Say they printed out 5 winning tickets and 1,850 tickets total. When you simplify that you get 1 winning ticket for every 370 non-winning tickets. It would be possible for a person to get all 5 in a row but really, really, really, really, unlikely.
Latest Answers