at a factory that produces pistons for cars, machine 1 produced 308 satisfactory pistons and 92 unsatisfactory pistons today. machine 2 produced 234 satisfactory pistons and 156 unsatisfactory pistons today. suppose that one piston from machine 1 and one piston from machine 2 are chosen at random from todays batch. what is the probability that the piston chosen from machine 1 is satisfactory and the piston chosen from machine 2 is unsatisfactory?

do not round your answer. (if necessary, consult a list of formulas.)

Question

at a factory that produces pistons for cars, machine 1 produced 308 satisfactory pistons and 92 unsatisfactory pistons today. machine 2 produced 234 satisfactory pistons and 156 unsatisfactory pistons today. suppose that one piston from machine 1 and one piston from machine 2 are chosen at random from todays batch. what is the probability that the piston chosen from machine 1 is satisfactory and the piston chosen from machine 2 is unsatisfactory?

do not round your answer. (if necessary, consult a list of formulas.)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Probability of Events", "Independent Events Probability" ], "new_concepts": [], "current_concepts": [ "Probability of Events", "Independent Events Probability" ] } ## Calculate Machine 1 probability Using the *Probability of Events* knowledge point $$ \begin{aligned} &\text{Total pistons from Machine 1} = 308 + 92 = 400\ &P(\text{Satisfactory from Machine 1}) = \frac{308}{400} = 0.77 \end{aligned} $$ ## Calculate Machine 2 probability Using the *Probability of Events* knowledge point $$ \begin{aligned} &\text{Total pistons from Machine 2} = 234 + 156 = 390\ &P(\text{Unsatisfactory from Machine 2}) = \frac{156}{390} = 0.4 \end{aligned} $$ ## Calculate joint probability Using the *Independent Events Probability* knowledge point $$ \begin{aligned} P(\text{Satisfactory}_1 \cap \text{Unsatisfactory}_2) &= P(\text{Satisfactory}_1) \times P(\text{Unsatisfactory}_2) \ &= 0.77 \times 0.4 \ &= 0.308 \end{aligned} $$ At a factory that produces pistons for cars, Machine 1 produced 308 satisfactory pistons and 92 unsatisfactory pistons today. Machine 2 produced 234 satisfactory pistons and 156 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 ? Do not round your answer. 0.308 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Independent Events Probability" ] }

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Question

Explanation:

Calculate Machine 1 probability

Calculate Machine 2 probability

Calculate joint probability

Answer: