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A professional glassblower has a probability of \(0.06\) of a piece cracking during the cooling process (independently of other pieces). They have just successfully completed 8 pieces without any cracks. Let \(X\) be the random variable representing the rank of the first piece that cracks.
What is the probability that the glassblower successfully completes the next 12 pieces without any cracks? Round to three decimal places.
What is the probability that a piece cracks before the 15th piece? Round to three decimal places.
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