Chapter 6, Problem 20P

NO AI PLEASE

A professor teaches two sections of a course: • 70% of students are in Section 1, and 30% are in Section 2. • In Section 1, 90% of students pass the final exam. • In Section 2, 80% of students pass the final exam. A student is randomly selected. a) Draw a tree diagram to represent this situation. b) What is the probability that the selected student passes the exam? c) Given that a student failed, what is the probability they were from Section 1?

.. A factory has two machines, A and B. Machine A produces 60% of the parts, while Machine B produces 40%. Machine A produces defective parts 5% of the time, while Machine B produces defective parts 10% of the time. A randomly selected part from production is inspected. a) Draw a tree diagram to represent the probability of getting a defective part. b) What is the probability that a randomly selected part is defective? c) If a part is found to be defective, what is the probability it came from Machine A?

A Factory produces light bulbs from two different machines: Machine A and Machine B. The probability that a randomly selected light bulbs is from Machine A is 60%, and the probability that a light bulb is defective is 5%. Suppose that probability that a light bulb is defective given that it was made by Machine A is 0.05. Similarly, the probability that a light bulb is defective given that it was made by Machine B is 0.03. Are the events “the light bulb is from Machine A” and “the light bulb is defective” independent?

3 (10pts). A Factory produces light bulbs from two different machines: Machine A and Machine B. The probability that a randomly selected light bulbs is from Machine A is 60%, and the probability that a light bulb is defective is 5%. Suppose that probability that a light bulb is defective given that it was made by Machine A is 0.05. Similarly, the probability that a light bulb is defective given that it was made by Machine B is 0.03. Are the events "the light bulb is from Machine A" and "the light bulb is defective" independent?

Please see the followinggn image

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Can you solve the following problem and show how the answer was found:

Can you solve the following problem and show how the answer was found: