So let’s look at the math. What is the equation for the probability that all those steps happened?
“All” ought to be a sum, right? A total? Add up the probability of each step and you should know how likely it is that JE existed, right?
A1 + A2 + A3 + A4 + A5 + A6 + A7 + A8 = Σ = probability.
When you’re evaluating a set of proposals for their combined truth, a truth table can be useful. If you’re adding them up, the truth table you have to use is this.
A1 A2 A1+A2
T T T
F T T
T F T
F F F
Some of you just had an “a-ha” moment. You know that this is a truth table for an OR function in logic. “Or” means alternatives. If you want to calculate the probability of DH this way, all of the steps have to be options. Producing JEDP went through one of those steps to the exclusion of the others.
Notice that, since the total probability can’t be greater than 1 (100%), the total is split up among the options, none of which has a probability of 1 (100%). You have two options flipping a coin; each of them has a 50% probability. If you have a die, each of the six sides has a 16.7% probability of coming up on any given throw. If you’re going to calculate the probability of JE this way, each of the 8 steps has to be an option. Once you pick one of the options, you’re done. Since none of the optional steps has a probability of 1 (100%), the probability of DH being true is limited to something below absolute fact.
But if those steps are all required, you need a different truth table.
A1 A2 A1 AND A2
T T T
F T F
T F F
F F F
If you replace the letters with “0” for F and “1” for T, you will see what is happening here. The zeroes in the rightmost column reflect a multiplication, not an addition; anything multiplied by 0 is 0. If a required step is false, and you have to multiply it by another required step, it doesn’t matter if the “other” step actually happened. The probability of both steps happening is 0, or No, or False, because one of them didn’t happen.
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