Question

at a factory that produces pistons for cars machine 1 produce 648 satisfactory pistons and 162 and satisfactory Pistons today machine two produced 560 and satisfactory Pistons and 140 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 1is satisfactory and the piston chosen from machine 2 is unsatisfactory?​

Answer 1

To find the probability that the piston chosen from machine 1 is satisfactory and the piston chosen from machine 2 is unsatisfactory, we can use the formula for conditional probability:
P(A and B) = P(A) * P(B|A)

where A is the event that the piston chosen from machine 1 is satisfactory and B is the event that the piston chosen from machine 2 is unsatisfactory.

We know that:
- P(A) = 648 satisfactory pistons / (648 satisfactory pistons + 162 unsatisfactory pistons) = 648/810
- P(B|A) = 140 unsatisfactory pistons / (560 satisfactory pistons + 140 unsatisfactory pistons) = 140/700

Therefore,
P(A and B) = (648/810) * (140/700) = 0.097

So, the probability that the piston chosen from machine 1 is satisfactory and the piston chosen from machine 2 is unsatisfactory is 0.097.