A system consists of two components. The probability that the second component functions in a satisfactory manner during its design life is 0.9, the probability that at least one of the two components does so is 0.96, and the probability that both components do so is 0.75. What is the probability that the second component functions in a satisfactory manner if it is given that the first component functions in a satisfactory manner throughout its design life?

Problem 3

The breakdown voltage of a randomly chosen diode of a certain type is known to be normally distributed with mean value 40 V and standard deviation 1.5 V.

(a)

What is the probability that the voltage of a single diode is between 39 and 42?

(b)

What value is such that only 20% of all diodes have voltage exceeding that value?

(c)

If four diodes are independently selected, what is the probability that at least one has a voltage between 39 and 42?

Problem 4

Suppose small aircraft arrive at a certain airport according to a Poisson process with rate per hour.

(a)

What is the probability that at least 2 small aircraft arrive during a 1-hour period?