Assuming that the die is perfectly balanced and weighted, and assuming that our throw was fair, you have a 1/6 chance of getting a five. Same with all the other numbers: a fair throw of a fair die has a 1/6 chance of producing any given number.
However, it will always produce a number. The odds of getting any given number are 1/6; the odds of getting any number at all are 6/6. The difference between the odds that something will happen and the odds that one specific thing will happen is an important one. The difference becomes more apparent with lower orders of probability: if I throw my die three times in a row, the odds of getting any specific sequence of numbers is 1/216: there are 216 possible sequences from 1:1:1, 1:1:2, 1:1:3 all the way to 6:6:6, and roughly equal odds of getting any given one of them. However, throw the die three times and you will ALWAYS get a sequence of three numbers.
The odds that you will get a combination of numbers are very, very high. The odds that you will get a specific set of numbers are very, very low.
Likewise, imagine a lottery: a million people buy tickets, and out of them one is declared a winner. The odds of any given person winning are 1/1,000,000. But the odds of someone winning are 1/1--someone always wins.
The odds that someone will win are very, very high. The odds that a specific person will win are very, very low.
So with that in mind, let's read a paragraph from Richard Dawkins:
The odds of arriving at the same 64:21 (64 codons: 21 amino acids) mapping twice by chance are less than one in a million million million million million. Yet the genetic code is in fact identical in all animals, plants and bacteria that have ever been looked at. All earthly living things are certainly descended from a single ancestor.So what's he saying there? If you have DNA, and you map to amino acids, then you will get a combination. If you throw a die three times, then you will get a series of numbers. If you set up a lottery, you will have a winner. Nothing remarkable about that. Nor is there anything particularly remarkable in it taking the specific form that it did: I rolled a die just now and got 2-5-5; so-and-so won the lottery; our codons map to amino acids the way that they do: so what? Since the outcome must always be something, and since all outcomes are equally probable, there is nothing remarkable about any given outcome.
So: getting a coding isn't remarkable. However, says Dawkins, all life on Earth uses the same coding. There are two explanations: either all life on Earth stems from a common origin, or else life had multiple origins which all happened to result in the same coding. However, getting something is easy; getting something specific is hard: roll a die and you will get three numbers, but the odds of getting the same numbers again is 1/216. Set up a million-man lottery and you will have a winner, but the odds of getting the same winner again is 1/1,000,000. Map codons to amino acids and you will get a coding, but the odds of getting the same coding again ... well, you get the idea. In the case of the coding it is frankly impossible; life must have a common origin.
So, when a friend-of-a-friend on Facebook mentioned that "Probe Ministries helps me sort through all the muck," I googled it to have a look. I clicked on 'Faith and Science', then 'Origins', and clicked the first article. There, I found the Dawkins quote mentioned and the following critique:
So it is reasonable to use probability to indicate that the code could not have arisen twice, but there is no discussion of the probability of the code arising by chance even once. A curious omission! If one tried to counter with such a question, Dawkins would predictably fall back on the assumption of naturalism that since we know only natural processes are available for the origin of anything, the genetic code must have somehow beaten the odds.The eternal question naturally arises: stupid or evil? Do they really have this poor a grasp of probability? Or are they charlatans deliberately preying on those who do?