I would pick A and D.
Reason for picking A: With A you know that there is a guaranteed 30% likelihood of winning so the only gamble you are making is whether you pull out of the of thirty red balls. With option B however you are essentially making two distinct gambles - the first that there are more than 30 black balls (as this would be required for option B to be the better of the two) and that you draw one of these balls. Personally I would prefer to bet on the guaranteed 30% chance. [As a side note, if the individual who handed you the bag is the same one you are making the bets with then they would have motivation to put less than 30 black balls in the bag anyway, making option A an even better choice]
Reason for picking D: Selecting option D means that you have a guaranteed 70% likelihood of winning as we know that all of the balls that are not red are either black of yellow. While there is the potential for this group to be mostly comprised of yellow balls (which would mean C would objectively be the better bet) there is also the potential for there to be mostly black balls. I would again select the more secure option, that being the 70% guaranteed chance of success.
I think the answers are in pairs.
If you pick gamble A and win then you should then pick gamble D for your second gamble.
The chance of gamble c winning as a stand-alone bet would be 30 (red balls) + 1-59 (yellow balls, assuming there is at least one yellow ball) or 30 + 0-60 if there are allowed to be zero black or yellow balls whereas the odds for gamble D are 60/90 as a stand-alone bet. These odds seem equal BUT if you removed one red ball when you won on gamble A then that swings the odds in favour of gamble D because the equation is now 29 + 1-59 vs 60/90.
If you pick gamble A and lose, the reverse is true and you should thus pick gamble C.
I am not sure if you published your question in order to practice your Japanese or your statistics & probability skills.. However I will try to answer.
The distribution of the chance to get a red ball deals with risk: the probability is known;
while the distributions of the chances to get either a black or a yellow ball deals with uncertainty: the probability is unknown. From symmetric considerations we may assume that we have equal numbers of blacks and yellow, but we don't know that for sure.
Practically I would say that the chances of A and B and of C and D are equal;
however, note that A deals with risk, B with uncertainty, C with a mixture of risk and uncertainty, and D with risk (we know the probability of black or yellow!).
