

Ask HN: Are chances of winning the lottery really that small? - robot

Yesterday afternoon I went to play the lottery card that my mother gave me while I was heading for the gym. While returning home I searched for a lottery play point on the street. She seldomly asks for it and I seldomly do this. I played it, paid around $5 (I'm in Turkey, 9 liras) and headed back home.<p>This morning we found out that she got 5 out of 6 numbers right. She won around $1500. I thought, what are the chances?<p>In Turkey its simple, there are 6 numbers that you need to get right, numbers 1 to 49 for each 6 slots. So the chance of getting 5 numbers right should be 1/49 * 1/49 ... which is 1/49^5 right? and that makes 1 in 282,475,249. That is one in 282 million 475 thousand 249th.<p>I find this to be a very low number. Even 1 in 1000 is very low. Now, I know that my Aunt, 10 years ago had hit 5 out of 6 numbers, too.<p>So what does this make, the chances are 1/282 millionth, yet every now and then someone in my close family hits it? It feels like there is some other forces of nature than pure chances in this. From Mr. Murphy: "Anything that can go wrong will go wrong" or the way I like to phrase it "If something can happen, it will happen".
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cd34
You've defined the number of permutations if each number can be picked more
than once not the number of combinations. Unless the numbers need to be picked
in order:

49 * 48 * 47 * 46 * 45 * 44 (each time you pick, there is one fewer item in
the pool)

But, since the order in which the items are picked isn't important:

10068347520 (product above) / (6 * 5 * 4 * 3 * 2 * 1)

or

1:13983816

Your odds for winning five out of six would be calculated the same way:

49 * 48 * 47 * 46 * 45 / (5 * 4 * 3 * 2 * 1)

or

1:1906884 - roughly 1 in 2 million.

However, since she picked those numbers and won, do you know what the odds are
that those numbers will win again?

1:1906884 - roughly 1 in 2 million. Like a coin toss, yesterday's results have
no influence on today's results.

I consider those wins to be lucky, but, I certainly wouldn't start throwing
cash at the lottery expecting similar wins.

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rhino42
Consider selection bias: You'll only hear about the people who won. Those who
bought a ticket and lost say nothing, because everyone knows that the chances
of winning a lottery are dismal to say the least. So you only hear about
winners!

