A lathe machine it produces solid parts with 80% probability. This turning machine continues to produce until the first defective part is produced. a) What is the probability distribution of the number of productions made until the first defective part is produced? b) What is the probability that the first defective part will show up in the 6th production? c) the selling price of the intact part is 80 TL and the damaged parts are sold as scrap for 10 TL. Processing cost of each piece is 30 TL. Your profit (one in gain random variable.) Find the probability function and the expected payoff.

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