Bag A holds 3 red and 2 yellow balls. Bag B holds 5 red and 4 yellow balls. One ball is to be drawn at random from one bag. Which bag offers the better chance of a red ball?

A probability is a proportion, so the bags must be compared by fractions, not by counts: Bag A offers 3/5 and Bag B offers 5/9. Over a common denominator these are 27/45 and 25/45, so Bag A is better, though only just. Bag B does hold more red balls, and more balls in total, but it holds correspondingly more yellow ones too, and a bigger bag is no advantage in itself. The subtlest wrong answer is the one that notes that each bag holds exactly one more red ball than yellow — true, but a lead of one counts for more in a bag of 5 than in a bag of 9, which is precisely why the DIFFERENCE between the counts settles nothing and only the ratio does.