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Alice and Bob play the following game: they each have a coin that shows "heads" with probability p and "tails" with probability q = 1 - p , where 0 < p < 1. Now, they both keep flipping their coins at the same time. The first player to flip "heads" while the other player gets "tails" wins. (This means that if both players flip "heads" or both flip "tails" in the same round, nobody wins and the game carries on.)
(a) What is the probability that Alice wins? Simplify your answer as much as possible
(b) Let Ai be the event that the game takes i or less turns. Determine P(Ai) for every i∈N
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A local business knows that 30% of their customers use a credit card to pay for their purchase. Suppose a sample of 85 customers is selected.
Each day, the United States Customs Service has historically intercepted about $28 million in contraband goods being smuggled into the country
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