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"by random draw" is a correct and usable part of a sentence in written English.
It is used to indicate that something has been chosen or selected at random. Example: "The winner of the raffle was chosen by random draw, with each ticket having an equal chance of being selected."
Exact(10)
In amateur tournaments, matchups are decided by random draw just before a fight.
The current European member Peter van den Bossche, for example, recently was selected (by random draw) to be on a new appeals panel pitting the U.S. (defending Boeing) against the European Union (defending Airbus) regarding aircraft subsidies.
Tickets for this year's Proms in the Park in the grounds of Castle Coole, outside Enniskillen, have now been allocated by random draw.
Drawing on a multiyear qualitative study of five circuit courts, including in-depth interviews with thirty-five judges and senior administrators, I show that strictly random selection is a myth, and an improbable one at that in many instances, it would have been impossible as a practical matter for the courts studied here to create their panels by random draw.
She's asking folks to donate to a GoFundMe -- the entire amount of which will be donated to one of the groups that receives Wildlife Rescue Nests (that group will be selected, she says, by random draw).
An incentive prize was offered by random draw.
Similar(50)
Then as now, state election law called for breaking ties by random drawing.
Of these, we selected by random drawing the 50 winners listed below.
The last — and perhaps only — time Virginia decided an election by random drawing was in 1971, to settle a tie in a race in Fairfax for a House seat.
Finally, the method itself was tested using a simulation in which the actual dates of implementing the e-prescription system was replaced by random draws of assumed interventions at different dates.
We generate the sets of n t =n c =200 trial outcomes of the treatment and control groups by random draws from respectively (mathcal {N}(1,5)) and (mathcal {N}(0,5)).
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com