Choice And Chance

Cover Choice And Chance
Choice And Chance
William Allen Whitworth
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A gives a true report four times out of five, B three times out of five, and C five times out of seven. If B and C agree in reporting that an experi- ment failed which A reports to have succeeded, what is the chance that the experiment succeeded ?
Answer. The chance that the given reports should be made upon the experiment having succeeded is 1422 16 2 ' C 5 X 5 :C 7' r 350' The chance that the given reports should be made on the experiment having failed is 1135 15 255' 7' r 350' The a priori c
...hance that in one way or other the given reports should be made is 16 15 31 +, or - . 350 350 ' 350 132 CHANCE.
But, a posteriori, this is certain, or the chance is multiplied by -gj- . Hence, also, the chance of each way in which the reports could be made is multiplied , 350 bv si- Therefore, a posteriori, the chance that the experi- ment succeeded is 16 350 16 350 X 31 ' r 81 ' We will conclude this chapter with some illustrations of the principles of probability, drawn from the game of whist.


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