RE: Your views on MARRIAGE
July 11, 2015 at 2:07 am
(This post was last modified: July 11, 2015 at 4:07 am by robvalue.)
(July 9, 2015 at 7:06 pm)pocaracas Wrote:(July 9, 2015 at 7:01 pm)Mr.wizard Wrote: Why does one cheating spouse out of ten put you at more of a risk then one cheating spouse out of one?
In 10 spouses, odds are higher that one of them will cheat you than with just one spouse.
If 10% of all people cheat, then, if you have 10 spouses, one of them is 100% likely to cheat, statistically speaking.
But if you only have 1 spouse, you have a 10% chance of having a cheating spouse.
The point being made here is valid, but I'd like to address the mathematics

In the above scenario, if we say that someone has a 10% chance of cheating at some point in their life:
The probability that at least one of them cheats at some point = 1 - The probability than none of them ever cheat
[They are exclusive and exhaustive events and so cover all possibilities with no overlap]
This probability, assuming all the people act independently is then:
1 - (90%)^10 = 1 - 0.3486784401... = 0.65 [To two decimal places. We need 10 non-cheaters in a row so we multiple their probability]
So the probability that at least one of the group cheats at some point in their life is slightly under two thirds.
What could instead be said is that the average number of people from the 10 who will cheat at some point in their life will be 1. This is probably what was meant in the first place to be fair

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