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Probability class of mathematical problems
1) Playing twice means playing twice and losing twice.

P=0.8*0.8*0.2*0.2 This is 1, and the probability of the second 3 or 4 misses.

There are six other categories that won the prize twice.

p = 0.8 * 0.8 * 0.2 * 0.2 * 6 = 0. 1536

2) The probability of all misses is 0.2*0.2*0.2*0.2.

At least one hit p =1-0.2 * 0.2 * 0.2 * 0.2 = 0.9984.