Actually, the Birthday paradox is a different problem, the chance two people have the same birthday: https://en.wikipedia.org/wiki/Birthday_problem
This is also known as the “Birthday Paradox”, because while the chances that a random persons birthday is today is 1/365, put 20 people in a room, and the chance that no ones birthday is today is (364/365)²⁰ =~ 0.95, or a surprising 5% chance that today is the birthday of at least one of those 20 people.
I am very familiar with this model because it is also essential for computing probability of equipment failure. https://eventhelix.com/RealtimeMantra/FaultHandling/system_reliability_availability.htm
p = probability of heads = 0.5
probability of both coins heads: 0.5 * 0.5 = 0.25
The probability is not double. If p is the probability of a man under one bed, then (1-p) is the probability of no man under one bed, and (1-p)(1-p) is the probability of no man under either bed, and 1-(1-p)(1-p) is the probability of a man under either bed.
Although, this does approximate doubling for the vanishingly small probabilities we are talking about in Lucille’s case, for more measurable probabilities (or more beds), it does not. E.g. if there is a 20% chance of a man under one bed, then the chance of a man under either bed is 1-(0.8*0.8) or 36%.
This is extremely important when it comes to what is sold as “safe sex”. If your birth control / protection is 99.9% effective, but you use it 52 times in a year, it has to be effective all 52 times to be effective over all (ignoring cycles, which complicate the example but do not change the principle). The probability of all 52 times being effective is .999⁵² or 95%. After two years, the overall effectiveness is 90%.
An unexpected baby can be a blessing, but this much ignored mathematical fact is much more troublesome when it comes to alleged protection from diseases transmitted by promiscuity.
Yes, all regulation favors the incumbents. As someone working on adding members to my local mesh network, I dread Net Neutrality making my amateur efforts illegal…
We tried a “dairy free cheesecake”, which turned out to be a thick coconut milk mousse over a rice cracker crust. It was frozen, and the first attempt to bypass the recommended 6 hour thawing process with the microwave was clearly an overdose. It became a rice cracker floating in a puddle of semi-clear coconut gel.
“Net neutrality” solves a problem that only affects so called “unlimited” access plans. When you actually pay for bandwidth used, the last thing an ISP wants to do is block or throttle your packets in any way – doing so would literally keep money out of their pocket. (“Unlimited” plans are what economists call “perverse incentives” for both customers and providers.)
The real problem is that “unlimited” internet is a meaningless marketing term, like “organic” food (all food is organic in a literal sense). And like with “organic”, the Constitutional role of the Federal government under the Weights and Measures clause is to give a concrete definition to the term.
What should happen is for Congress to define what “unlimited” internet actually means – and probably include all or most of the features demanded by “Net Neutrality” (itself a meaningless marketing term) advocates. I.e., when offering an “unlimited” plan, you can’t throttle, port block, or sell packet prioritization.
There are really harmful aspects of applying Net Neutrality to all access plans. Like the part about making paying for priority illegal. When making VOIP (phone) calls through the internet, for instance, you might want to set the QoS (Quality of Service) flags on those packets and pay extra to reduce latency.
Even the worst abuses of current practice are good things when properly labeled. There could be a “Movie Watchers Plan” – where you get cheap, high bandwidth connections to content providers that pay to participate – and “as available” for everything else.
Again, enforcing truth in labeling is a Constitutional function of the Federal government. Telling private companies how to manage their networks is not.
“Wipes out all bad people” – that would be everyone.
Most of the time, people come back full of stories and experiences they are dying to share. In the old days, they would have slides, and you hope they don’t invite you to a slide show! But the traveler is usually too polite to bore people uninvited, so as a gesture of kindness (or if you are really interested), you invite them to tell you their story.
However, people tend to ask in passing, without leaving time to actually tell any stories, and the traveler is then frustrated with being effectively asked for a one sentence summary. Some will respond with a grudging “fine”. Others will launch into their story anyway…