In a semiconductor manufacturing company, it is estimated that 0.15, 0.015, and 0.005 of failures are...

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In a semiconductor manufacturing company, it is estimated that 0.15, 0.015, and 0.005 of failures are conditional on high, medium and low contamination levels respectively. It is also estimated that in a particular production system, that 10%, 40%, and 50% of chips are ex- posed to high, medium and low levels of contamination respectively. Let H, M, and L represent high, medium and low levels of contamination respectively. Also let F represent failure. a. Represent the above scenario in a probability tree and make sure to name each arc (arrow) and each node (see week 3 the example we did). b. Calculate the probability of failure. Question 2: In a certain game, you have equal likelihood es) of winning or losing. When you win, you gain twice as much as your initial fortune. When you lose, you gain only half of your initial fortune. Assume that you started with W dollars. a. What is the expected gain? Hint: Begin with producing the probability mass function in a table form. b. If you play this game n INDEPENDENT times. What is the expected gain? Hint: Take these as n independent events and use the multiplication rule. Also notice that, for example, if you toss a coin three times, the P(HHH) is not 3P(H), instead it is P(H)³. In a semiconductor manufacturing company, it is estimated that 0.15, 0.015, and 0.005 of failures are conditional on high, medium and low contamination levels respectively. It is also estimated that in a particular production system, that 10%, 40%, and 50% of chips are ex- posed to high, medium and low levels of contamination respectively. Let H, M, and L represent high, medium and low levels of contamination respectively. Also let F represent failure. a. Represent the above scenario in a probability tree and make sure to name each arc (arrow) and each node (see week 3 the example we did). b. Calculate the probability of failure. Question 2: In a certain game, you have equal likelihood es) of winning or losing. When you win, you gain twice as much as your initial fortune. When you lose, you gain only half of your initial fortune. Assume that you started with W dollars. a. What is the expected gain? Hint: Begin with producing the probability mass function in a table form. b. If you play this game n INDEPENDENT times. What is the expected gain? Hint: Take these as n independent events and use the multiplication rule. Also notice that, for example, if you toss a coin three times, the P(HHH) is not 3P(H), instead it is P(H)³.