Question

At a factory that produces pistons for cars, Machine 1 produced 174 satisfactory pistons and 116 unsatisfactory pistons today. Machine 2 produced 180 satisfactory pistons and 20 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 satisfactory and the piston chosen from Machine 2 is unsatisfactory

Answer 1

`0.7` is the probability that the piston chosen from Machine 1 is satisfactory and the piston chosen from Machine 2 is unsatisfactory

Explanation:

The two events are independent of each other.

Hence the probability of choosing satisfactory piston from Machine 1 and unsatisfactory piston from Machine 2 is equal probability of choosing satisfactory piston from Machine 1 + probability of choosing unsatisfactory piston from Machine 2

Substituting the given values we get

Probability of choosing satisfactory piston from Machine 1 and unsatisfactory piston from Machine 2 =
`(174)/(174 +116) + (20)/(180 +20)`

=
`(174)/(174 +116) + (20)/(180 +20)`

=
`= (174)/(290) + (20)/(200)\\= 0.6 + 0.1\\= 0.7`