# A system contains two componen

A system contains two components, C and D, connected in parallel as shown in the diagram.

Assume C and D function independently. For the system to function, either C or D must function.

a. If the probability that C fails is 0.08 and the probability that D fails is 0.12, find the probability that the system functions.

b. If both C and D have probability p of failing, what must the value of p be so that the probability that the system functions is 0.99?

c. If three components are connected in parallel, function independently, and each has probability p of failing, what must the value of p be so that the probability that the system functions is 0.99?

d. If components function independently, and each component has probability 0.5 of failing, what is the minimum number of components that must be connected in parallel so that the probability that the system functions is at least 0.99?

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# A system contains two componen

A system contains two components, A and B, connected in series, as shown in the diagram.

Assume A and B function independently. For the system to function, both components must function.

a. If the probability that A fails is 0.05, and the probability that B fails is 0.03, find the probability that the system functions.

b. If both A and B have probability p of failing, what must the value of p be so that the probability that the system functions is 0.90?

c. If three components are connected in series, and each has probability p of failing, what must the value of p be so that the probability that the system functions is 0.90?

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# A system contains two componen

A system contains two components, A and B. The system will function only if both components function. The probability that A functions is 0.98, the probability that B functions is 0.95, and the probability that either A or B functions is 0.99. What is the probability that the system functions? Human blood may contain either or both of two antigens, A and B. Blood that contains only the A antigen is called type A, blood that contains only the B antigen is called type B, blood that contains both antigens is called type AB, and blood that contains neither antigen is called type O. At a certain blood bank, 35% of the blood donors have type A blood, 10% have type B, and 5% have type AB.

a. What is the probability that a randomly chosen blood donor is type O?

b. A recipient with type A blood may safely receive blood from a donor whose blood does not contain the B antigen. What is the probability that a randomly chosen blood donor may donate to a recipient with type A blood?

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