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  1. There's a way to understand that the odds are equal for both bowls without doing any math (for both the one poison apple = death and the two poison apples = death variants). Label the apples in each bowl as either common (C) or rare (R), so each bowl has CCCRR. For bowl 1, the common apples are poisonous and the rare apples are not. For bowl 2 the opposite. When you choose the apples that you are going to eat (from whichever bowl) you are going to divide the apples into two groups - those you will eat, and those you won't. In the one apple = death variant, the only way to survive is to divide the apples into two specific groups: CCC in one group and RR in the other. This is true for bowl 1 and bowl 2 - which means that the probability is the same for both. For bowl 1, you will then eat the two apples (both rare/nonpoisonous). For bowl 2, you will then eat the three apples (all common/nonpoisonous apples). In the two apples = death variant, you will only die in one way: if you divide the apples such that the group of two apples contains two common apples. That is, CRR in one group and CC in the other. Again, this is true for bowl 1 and bowl 2, so the probabilities are the same. (The order of apples doesn't matter within the groups because we will either eat all or none of the apples in a given group.) If we choose bowl 1, we eat the smaller group, and only die if that smaller group contains two common/poisonous apples. If we choose bowl 2, we eat the larger group and will only die if the smaller group (the one we didn't eat) contains two common/nonpoisonous apples (as this means that both of the poisonous apples were in the group we ate). So, without doing any math, you can see that the probabilities are equal, even if you can't tell what the probabilities are. This understanding of the problem also makes calculating the probability of death easier, if you want to calculate it. For one apple = death, you only survive if the small group has two rare apples. 2/5 * 1/4 = 1/10 (10% survival rate/90% survival rate) For two apples = death, you only die if the small group has two common apples. 3/5 * 2/4 = 3/10 (30% death rate/70% survival rate)
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