How can I convert the percentage 0.000007151123842% into odds, so the outcome would be 1 in 13983816. Basically, I am looking for a way to convert any positive percentage into odds so the outcome gives me 1 in N.
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To convert something to be "1 in N", you simply take the reciprocal. In this case, you have it correct:
$$ \frac{1}{0.00000007151123842} = 13,983,816 $$
So you get an event that happens "1 in 13,983,816" tries.
Odds are a bit different in that they usually give the ratio between two events happening. For example 1:1 (pronounced "1 to 1") odds means a 50% chance of that event happening and is equivalent to "1 in 2". A 20% chance would be 1:4. So, you'll subtract 1 from the reciprocal to get odds of 1:13,983,815.
In general, the odds are
$$ 1:\bigg(\frac{1}{p}-1\bigg) $$
where $p$ is the probability of the event expressed as a decimal.
Poisson Fish
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Hmm, every calculator I try gives me a different result, even google: https://www.google.com/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=1%20%2F%200.000007151123842 Am I missing the obvious here? – Jürgen Oct 07 '15 at 20:05
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That's because it must be expressed as a decimal. 0.000007151123842%=0.00000007151123842. – Poisson Fish Oct 07 '15 at 20:06
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Even though frowned upon, I still want to thank you for your thorough explanation, truly much appreciated! I can't believe the solution was so simple. – Jürgen Oct 07 '15 at 20:11
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@user1646633: If you want to thank him, you should also upvote the answer (click on the up-arrow above the answer's score), which you now have enough reputation to do. – hmakholm left over Monica Oct 07 '15 at 20:19
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@Henning Makholm Thanks for pointing that out, I did not know I now have enough, yesterday it did not work yet. – Jürgen Oct 07 '15 at 20:20
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@user1646633, what is frowned upon? – Poisson Fish Oct 07 '15 at 20:57
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@PoissonFish Thanking someone in comments, I read that we should refrain from that. – Jürgen Oct 08 '15 at 09:31
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Ah gotcha. I'm not going to frown upon it :) – Poisson Fish Oct 08 '15 at 14:28