A trial has just resulted in a hung jury because eight members of the jury were in favor of a guilty verdict and the other four were for acquittal. If the jurors leave the jury room in random order and each of the first four leaving the room is accosted by a reporter in quest of an interview, what is the pmf of X = the number of jurors favoring acquittal among those interviewed? How many of those favoring acquittal do you expect to be

Answer : Step 1 of 2 : Given, A trial has just resulted in a hung jury because eight members of the jury were in favor of a guilty verdict and the other four were for acquittal. If the jurors leave the jury room in random order and each of the first four leaving the room is accosted by a reporter in quest of an interview, The claim is to find the pmf of X = the number of jurors favoring acquittal among those interviewed and How many of those favoring acquittal do you expect to be. The population N= 12 total jurors, there are total of success is M = 4 jurors of acquittal, and sample size of n = 4. There are five possible values of x, that is 0, 1, 2, 3, 4, (0) 4 x P(x = 0) = ( ) 4 = 0.1414 4 8 (1) 4 1 P(x = 1) = ( ) 4 = 0.4525 4 8 (2) 4 2 P(x = 2) = ( ) 4 = 0.3394 4 8 (3) 4 3 P(x = 3) = 4 ) = 0.0646 4 8 P(x = 4) = (4)4 4 (4) = 0.0020