occurring by chance

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The team sifted through millions of letters of genetic code using a computer program developed to calculate the probability of convergent changes occurring by chance, so they could reliably identify 'odd-man-out' genes.
In simplistic terms, statistical significance measures the likelihood that any apparent differences between study data are real and not occurring by chance.
A distinction is made between deliberate attempts to create such windows and those occurring by chance in published text.
The probability of that outcome occurring by chance is about one in 10 quadrillion.
There, the court found accident to be defined as "an event or condition occurring by chance or arising from unknown or remote causes" and "lack of intention or necessity.
Justice Rubin dissented on the grounds that the lack of a statistical probability analysis of a DNA match occurring by chance should have been fatal to the admissibility of the inconclusive DNA evidence.
The alternative explanation for the improbable conditions that make intelligent life possible is that rather than occurring by chance, they reflect the action of the One who created the universe.
Such speculations have little scientific predictive value in the absence of an explanation for what factors and conditions cause the occurrence of quantum events that have essentially zero probability of occurring by chance.
The dictionary defines Accident as being a mishap or event occurring by chance whereas Incident is defined as being an event or occurrence.
statistician who testified at the grand jury hearing said the scores were almost certainly fraudulently obtained and explained the odds of such a feat occurring by chance were ``about three in 10 billion.
The probability of this order occurring by chance without an active intelligence cannot be explained.
1% probability of this improvement occurring by chance (p<0.