At a factory that produces pistons for cars, Machine 1 produced 413 satisfactory pistons and 177 unsatisfactory pistons today. Machine 2 produced 350 satisfactory pistons and 150 unsatisfactory pistons today. Suppose that one piston from Machine 1 and one piston from Machine 2 are chosen at random from today's batch. What is the probability that the piston chosen from Machine 1 is unsatisfactory and the piston chosen from Machine 2 is satisfactory ?

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artessaw artessaw

07-02-2015
Mathematics

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At a factory that produces pistons for cars, Machine 1 produced 413 satisfactory pistons and 177 unsatisfactory pistons today. Machine 2 produced 350 satisfactory pistons and 150 unsatisfactory pistons today. Suppose that one piston from Machine 1 and one piston from Machine 2 are chosen at random from today's batch. What is the probability that the piston chosen from Machine 1 is unsatisfactory and the piston chosen from Machine 2 is satisfactory ?

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The probability of two independent events is the product of the probability of each event. Then calculate the probabilities of each event and multiply them. Probability that the piston chosen from Machine 1 is unsatisfactory is 177 out of (177 + 413 ) = 177 / (590) = 0.3. Probability that the piston chosen from Machine 2 is satisfactory = 350 / (350 + 150 ) = 350 / 500 = 0.7. Then the joint probability is 0.3 * 0.7 = 0.21. Answer: 0.21