Imagine a friend hands you a deck of cards, claiming that it is NOT an untouched deck of cards which had just been removed from the box -- i.e., so that the top card would be the Ace of Clubs, and the very next card would be the 2 of Clubs, etc. -- but that, instead, it is a well-shuffled deck.
Your friend then asks "Do you believe me when I tell you that that deck of cards is well-shuffled?"
Practical Proof
If you didn't know about probability, you may start turning over cards, noticing that the Ace of Clubs was the top card, and the 2 of Clubs was next, and then the 3 of Clubs was the very next card, etc.
As the first 3 cards come out in order (A-2-3 of Clubs), your friend says "That's just a coinicidence. It is still possible that I shuffled that deck well. You can't judge me based on that level of evidence."
By the time that the 3 of Clubs shows up in this series though, the probability of the evidence has already reduced down to 1/132,600, or p = 0.0000 075.
In legal paternity cases argued in court, just 99.99% confidence (p = 0.0001) is already considered to be "practical proof" -- and men are court-ordered to pay child support when the evidence is THAT strong that they are the father.
Because you want to be sure that your friend is lying before you call him a liar (no sense in burning bridges before dishonesty is "proven"), you keep turning over cards.
Lightning Strikes
... 4 of Clubs ... [your friend repeats: "It's STILL just a coincidence. It is STILL possible that I shuffled that deck well. You can't judge me based on that level of evidence."]
But by the time the 4 of Clubs shows up in perfect order, along with the other three cards, then you are now below the annual probability of being struck by lightning (1 chance in 1.2 million).
Because you want to be REALLY sure your friend is lying before you burn a bridge with him, you keep turning over cards ...
Solar Lifetimes
... 5 of Clubs, 6 of Clubs, 7 of Clubs, 8 of Clubs ... and then you stop at the 8 of Clubs and look up to your friend. You recall from astrophysics class that celestial stars like our sun burn normally for 4 trillion days before all of the core hydrogen is used up.
You say, this time with confidence: "It would be more likely for the sun to fully burn up all of its core hydrogen in just the next 24 hours -- than for that last card to have been the 8 of Clubs."
Your friend says "So! So what?"
But you say "If it is more probable that the sun will 'burn out' today than that are telling the truth, then I cannot, in good conscience, continue believing you."
Beyond 15 decimal places
Against all logical reasoning, you bite the bullet, extend even more trust to your friend, and turn over the ninth card --- and it is the 9 of Clubs.
From a well-shuffled deck, there is not even a 1 in 999 trillion chance that the first 9 cards are A-9 of Clubs in order.
Real-life application
Let's say that the highest paid US government official declares that a disease is 10 times worse than flu.
If true, then certain samples would have certain probability to be found in well-controlled natural experiments, such as the 7 COVID deaths found in the 3711 persons on board the Diamond Princess cruise ship in the spring of 2020.
Because median age on the cruise ship was 65, had flu attacked the ship, it would have killed, on average, 5 people. If COVID is 10 times worse than flu, then on average 50 people would have died from COVID.
The outcome can be modeled by a Poisson distribution (possible number of occurrences per interval; given average or expected occurrence per interval).
The probability of a sample of 7 or less deaths, when the null-hypothesized Poisson mean is 50 deaths, is
p = 0.0000 0000 0000 034 (~ 1 chance in 29 trillion)
Fauci made what can be called an "8 of Clubs" statement (a '1-in-30-trillion' statement). Our task is to decide whether he was lying. We decide the financial fate of potential fathers in court cases on much less evidence than we have to indicate that Fauci was lying.
It is more likely that our sun begins to turn into a Red Giant "today" (growing to a hundred-fold its current size) -- than that Fauci was actually telling the truth.
That probability has also been true for each of the ~700 days which have passed since he made the claim on 11 Mar 2020.
Almost every human decision made -- eg, get in car to attempt to make it safely to work, look both ways before crossing freeway to attempt to prevent being hit by a car, take aspirin to attempt to remove headache, etc. -- is made on less evidence than that which we have that Fauci was lying to the US public.
Image source and attribution [top image modified from original]
page URL: https://commons.wikimedia.org/wiki/File:Contemporary_playing_cards.svg
Attribution: Betzaar, CC BY-SA 3.0 https://creativecommons.org/licenses/by-sa/3.0, via Wikimedia Commons