A gambler claimed that he had loaded a die so that it would hardly ever come up 1. He said the outcomes of 1, 2, 3, 4, 5, 6 would have probabilities 1 20 , 1 6 , 1 6 , 1 6 , 1 6 and 1 6 respectively. Is this a probability distribution?

The man is left with one apple. Before the seventh gate, he had (1+1)x2, or 4 apples. Before the sixth gate, he had (4+1)x2, or 10 apples. Before that, he had (10+1)x2, or 22 apples. Thus, the number of apples he had is as follows:
1,4,10,22,46,94,190,382. So, he started with 382 apples
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