1. A circuit has three major components: A, B, and C. Component A operates independently of B and C. The components B and C are interdependent. It is known that the component A works properly 85% of the time; component B, 90% of the time; and component C, 95% of the time. However, if component C fails, there is a 75% chance that B will also fail. Assume that at least two parts must operate for the circuit to function. What is the probability that the circuit will function properly?
2. Suppose that the data in Table represent approximate distribution of blood type frequency in percentage of total population.
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Table
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Blood type
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O
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A
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B
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AB
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Frequency (%)
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45
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40
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10
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5
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Assume that the blood types are distributed the same in both male and female populations. Also assume that the blood types are independent of marriage.
(a) What is the probability that in a randomly chosen couple the wife has type B blood and the husband has type O blood?
(b) It is known that a person with type B blood can safely receive transfusions only from persons with type B or type O blood. What is the probability a husband has type B or type O blood? It is given that a woman has type B blood, what is the probability that her husband is an acceptable donor for her?