@Steve O 223475 wrote:
Hey statistics gurus – what are the odds that after 14 plays, only two appear on a random card?
’cause that’s me.
:confused:
I made it easier on myself. The first draw was actually one I needed. So the new question is: with 13 draws (without replacement) from a set of 74, what are the odds of only 1 of them being in the needed set of 24?
I brute-forced it and came up with something between 1:300 and 1:500. However, I know my method is flawed.
That said, I’m still curious about how to do the original probability, and also curious if my method is sort-of valid, and my answer is in the ballpark, since it’s been a long, long time since I took statistics.
Since I’m too lazy to do this the rigorous (or right) way but still wanted the distraction – some hand wavy calculations in the other direction:
1. Each card has 25 words out of a bank of 75, so you have 1/3 of the available words on your card.
2. That means 2/3 of the words are missing from your sheet.
3. Let’s just assume that each day is like a weighted coin flip – you’ve picked heads, but you only have a 1/3 chance of landing a heads, and 2/3 chance of landing tails. (This is the worst assumption of all because it treats each day’s odds as an independent event, but it’s early enough that this isn’t completely out of this world.) What are the odds you only got 2 heads in 14 attempts with this “unfair” coin?
Then abusing this as a binomial distribution, the “expected” number of words chosen to date you would have on your card would be between 4 and 5. Having 2 (or fewer) would be somewhat unlikely, but still a bit more than 1:10 (just over 10.5% for having 0, 1, or 2 matches, with exactly 2 being 7.8%)
Where the more rigorous calculation gets annoying is that, over 14 days, there are a total of 91 combinations of ways that you could have 2 matches just in terms of “matched on days x and y” and 16,384 ways you can arrange the simple “did I match” tied to each day. There are plenty of websites that go into detail on regular Bingo calculations (EV for the number of turns before a BINGO is called is apparently 41), but the math here isn’t quite the same since I think it’s one bank of 75 words rather than 5 banks of 15 words each for each column.
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