Question

At a factory that produces pistons for cars, Machine 1 produced 306 satisfactory pistons and 204 unsatisfactory pistons today. Machine 2 produced 385 satisfactory pistons and 115 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 ?

Answer 1

The probability that the piston chosen from Machine 1 is unsatisfactory and the piston chosen from Machine 2 is satisfactory is 308/1700.

Explanation:

The probability of selecting an unsatisfactory piston from Machine 1 is 204/510, because there are a total of 204 + 306 = 510 pistons produced by Machine 1, and 204 of them are unsatisfactory.

The probability of selecting a satisfactory piston from Machine 2 is 385/500, because there are a total of 385 + 115 = 500 pistons produced by Machine 2, and 385 of them are satisfactory.

To find the probability that both events occur, we multiply the probabilities:

P(unsatisfactory from Machine 1 and satisfactory from Machine 2) = (204/510) * (385/500)

Simplifying the expression, we get:

P(unsatisfactory from Machine 1 and satisfactory from Machine 2) = (4/17) * (77/100)

P(unsatisfactory from Machine 1 and satisfactory from Machine 2) = 308/1700

Therefore, the probability that the piston chosen from Machine 1 is unsatisfactory and the piston chosen from Machine 2 is satisfactory is 308/1700.