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Please show all work and all steps. 1.) Two cards are drawn from a standard 52-card...

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Basic Math

Please show all work and all steps.

1.) Two cards are drawn from a standard 52-card playing deck.What is the probability that the draw will yield an ace and a facecard?

2.) Articles coming through an inspection line are visuallyinspected by two successive inspectors. When a defective articlecomes through the inspection line, the probability that it gets bythe first inspector is .1. The second inspector will \"miss\" fiveout of ten of the defective items that get past the firstinspector. What is the probability that a defective item gets byboth inspectors?

3.) A diagnostic test for a disease is such that it (correctly)detects the disease in 90% of the individuals who actually have thedisease. Also, if a person does not have the disease, the test willreport that he or she does not have it with probability .9. Only 1%of the population has the disease in question. If a person ischosen at random from the population and the diagnostic testindicates that she has the disease, what is the conditionalprobability that she does, in fact, have the disease? Are yousurprised by the answer? Would you call this diagnostic testreliable?

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