Q1(8). There are 100 cards of the same shape in one deck. There are four different...

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Q1(8). There are 100 cards of the same shape in one deck. There are four different patterns. 20 cards' pattern is clubs, 25 cards' pattern is diamonds, 25 cards' pattern is spades and 30 cards' pattern is hearts. 1(4). You are blindfolded and asked to draw three cards from the deck without replacement. Calculate the probability that there is exactly one card of hearts pattern among the three cards. 2(4). You are blindfolded and asked to draw two cards from the deck with replacement. Calculate the probability that both are spades. Q2(12). Suppose the population defective rate of one product is 2%. Given the product is defective, the quality testing department will have probability 0.98 to label it as defective; for non-defective product, the quality testing department will have probability 0.05 to label it as defective. 1(4). For a randomly selected product, what is the probability of receiving a defective label after the test? 2(4). Given that the product received a defective label, what is the probability that the product is indeed defective? 3(4). Suppose two products are randomly sampled, what is the probability that only one of them receives defective label? Q1(8). There are 100 cards of the same shape in one deck. There are four different patterns. 20 cards' pattern is clubs, 25 cards' pattern is diamonds, 25 cards' pattern is spades and 30 cards' pattern is hearts. 1(4). You are blindfolded and asked to draw three cards from the deck without replacement. Calculate the probability that there is exactly one card of hearts pattern among the three cards. 2(4). You are blindfolded and asked to draw two cards from the deck with replacement. Calculate the probability that both are spades. Q2(12). Suppose the population defective rate of one product is 2%. Given the product is defective, the quality testing department will have probability 0.98 to label it as defective; for non-defective product, the quality testing department will have probability 0.05 to label it as defective. 1(4). For a randomly selected product, what is the probability of receiving a defective label after the test? 2(4). Given that the product received a defective label, what is the probability that the product is indeed defective? 3(4). Suppose two products are randomly sampled, what is the probability that only one of them receives defective label?

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