MB 3600 Homework -2 APPLICATION OF BAYES' THEOREM (use the tabular approach demonstrated in class) Problem - 1: A production manager for a manufacturing firm is supervising the machine setup for production of precision auto parts. The machine operator sets up the machine. If the machine is set up correctly, there is a 10% chance that a part produced by the machine will be defective. If the set up is incorrect, the chance that a produced part is defective rises to 40%. From past experience, the production manager knows that in 50% of the cases, the machine has been set up incorrectly by the operator. Before giving orders for the production of a large batch of auto parts, the manager instructs the operator to produce a sample part. The part turns out to be defective. What is the probability, based on the sample part being defective, that the machine was set up incorrectly? - i.e. what is: Probability (machine set up incorrectly | produced part is defective) Use the following definitions: C: event \"correct setup of machine\" IC: event \"incorrect setup of machine\" D: event \"produced part is defective\" Show your work and clearly explain your reasoning for your answer. Problem - 2: Taxicabs in a city are of 2 colors: Blue & Green. 85% of the cabs are Blue; 15% of them are Green A taxicab was involved in a hit and run accident last night. A witness identified the cab as Blue. The witness is given a series of vision tests by the police. The results indicate that he identifies the colors (blue & green) correctly 80% of the time. He fails the test 20% of the time. What is the probability that the witness correctly identified the color of the cab - i.e. what is: Probability (cab IS Blue | witness says that cab is Blue) Use the following definitions: A: event \"cab is Blue\" ~A: event \"cab is NOT Blue\" B: event \"witness says that cab is Blue\" Show your work and clearly explain your reasoning for your answer. APPLICATION OF PROBABILTY CONCEPTS and PROBABILITY TREE APPROACH (hint: continue building on the partial Probability Tree shown below) Problem - 3: This game involves two players: Player 1 and Player 2. There are 6 balls placed in a container, of which 2 are green and 4 are red. The objective of the game is for each player to take alternate turns and draw a single ball at a time (without putting it back into the container). The player who is the first to draw a green ball wins the game. Assume that Player 1 begins the game. What is the probability that Player 1 will be the winner? Hint