Two different factories both produce a certain computer part…

Two different factories both produce a certain computer part. The probability that a component from the first factory is defective is 2% and the probability that a component from the second factory is defective is 5%. In a supply of 180 parts, 100 were obtained from the first factory and 80 from the second factory.  Question: What is the probability that a part chosen at random from the 180 is from the first factory?

Consider the problem: A group consists of five adults and se…

Consider the problem: A group consists of five adults and seven teenagers. How many teams of five contain at least one adult? A student submits the following solution:  Step 1: Choose a subset of one man from the five men: 51{“version”:”1.1″,”math”:”51″} Step 2: Choose a subset of four others from the remaining eleven people: 114{“version”:”1.1″,”math”:”114″} By the Multiplication Rule, there are 5×330=1,650{“version”:”1.1″,”math”:”5×330=1,650″} five-person teams that contain at least one adult. Question: Is this solution correct? If not, what is the error in the student’s solution?  Note: It is not sufficient to simply state the correct answer if you believe the student’s answer is incorrect. You must explain the error in the student’s reasoning.