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A quality control machine tests computer chips until it detects a defective one. The probability that a chip is defective is \(0.04\). Let \(X\) be the random variable representing the number of chips tested to find the first defective one.
State the distribution followed by \(X\).
Represent the situation with a tree diagram for the first three chips tested and use it to find \(P(X=2)\).
Calculate \(P(X=5)\) and interpret the result.
Calculate \(P(X \leq 10)\) and interpret the result.
Calculate \(E(X)\) and interpret the result.
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