Today Puzzle #641
Puzzle No. 641– Friday 27 December
The British Jury system involves 12 jurors. In order to reach a verdict, at least 10 of the jurors must reach the same decision. Assuming independence of the jurors and a 75% likelihood of each juror finding a defendant guilty, what is the probability that the defendant would be found guilty by the jury overall?
Today’s #PuzzleForToday has been set by Dr Shaun Fitzgerald, Director of the Royal Institution and fellow of Girton College where Baroness Hale is Visitor
Click here for the answer
There is one way of all 12 jurors finding the defendant guilty, there are 12 ways with 11 jurors finding the defendant guilty, and 66 ways of 10 jurors doing so. The probability of the defendant being found guilty is therefore 0.7512 + 12x0.25x0.7511 + 66x0.252x0.7510 = 39%
(Interestingly, if the likelihood of each juror is greater than 91% then the probability of the jury overall is greater than that, whereas if it is less than 91% then the figure is lower.)