This is a notorious puzzle used by Bayesian to attack Frequentist (because the question itself only makes sense from Bayesian's pespective). If you use the basic +1 prior (2+1)/(3+1) > (5+1)/(8+1). So option 1 is harder. If you use the Jeffrey's prior, (2+0.5)/(3+0.5)>(5+0.5)/(8+0.5). So option 1 is still harder. However, even if you don't use prior 2/3 is still larger than 5/8. A trickier version is to compare 2/3 with 7/10: 2/3 < 7/10, but 3/4 >8/11, and 2.5/3.5 = 7.5/10.5
【在 b*****o 的大作中提到】 : This is a notorious puzzle used by Bayesian to attack Frequentist (because : the question itself only makes sense from Bayesian's pespective). : If you use the basic +1 prior (2+1)/(3+1) > (5+1)/(8+1). So option 1 is : harder. : If you use the Jeffrey's prior, (2+0.5)/(3+0.5)>(5+0.5)/(8+0.5). So : option 1 is still harder. : However, even if you don't use prior 2/3 is still larger than 5/8. : A trickier version is to compare 2/3 with 7/10: : 2/3 < 7/10, but 3/4 >8/11, and 2.5/3.5 = 7.5/10.5