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The key to this is to understand that in half of all cases where two aces were drawn, the second random step will pick the heart 1/2 the time.
Thus - the first step selects 5 out of 6 possible outcomes. In the second step, 4 of the 5 cases have fixed outcomes; the other (Aa) has two posssible outcomes.
Thus there are six possible final states:
1 a D showing a (1/5) 2 a d showing a (1/5) 3 A D showing A (1/5) 4 A d showing A (1/5) 6 A a showing a (1/10) 6 A a showing A (1/10)
The answer to the second question is yes in cases 2, 3, and 6. The collective probability of these cases is 1/5 + 1/5 + 1/10 = 1/2.
1/10 over 1/2 is 1/5.
What about expectations? A lot of "outsider" groups and movements assert that Come The Revolution. their superior wisdom/intellect/knowledge will be recognized and they will then have great wealth/status/power.
It's worked sometimes. And those who "get in on the ground floor" sometimes benefit extravagantly.
First, the Nazis were not stupid or incompetent. They didn't just yell at people, they persuaded. They formed a large and efficient media organization to push their program. In retrospect, much of what they advocated now seems obvious nonsense, but that's in retrospect: it was a lot more plausible at the time. The final success of the Nazis also occurred in the context of economic disaster. 25% unemployment tends to discredit orthodox, established doctrines. Did the Nazis screw up? Massively, in the end. But they would not have gotten in the position to make those mistakes without doing a lot of difficult things correctly first.
Second, "no group of people has managed to achieve anything even remotely similar using... rationality [and] deliberative thought"? How about the Founders of the United States? In fifteen years (1775-1790) they took their country from being the exploited colony of a Great Power to being a prosperous sovereign nation with the most advanced system of government in the world. And they were rational men and deliberate thinkers,