Probability of independent events: Decimal answers

Question

At a factory that produces pistons for cars, Machine 1 produced 369 satisfactory pistons and 41 unsatisfactory pistons today. Machine 2 produced 332 satisfactory pistons and 68 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 ?

Do not round your answer.

Answer 1

Event A = piston chosen from machine 1 unsatisfactory

Event B = piston chosen from machine 2 unsatisfactory

Since A and B are independent events

P(Event A & Event B both occur) = P(A) * P(B)

P(A) = number unsatisfactory/total number = 41 / (41 + 369) = 0.1

P(B) = 68 / (68 + 332) = 0.17

P(A and B) = 0.1 * 0.17 = 0.017