Exam 5: The Dynamics of Population: An Overview

A single die is rolled, twice. What is the probability of obtaining the 3 on either of the two rolls of the die?

Two dice are rolled. What is the probability of not getting a 7 or 11 on the first two rolls of the dice?

If an engineer has 2 switches and 4 bulbs in a container, what is the probability of the engineer choosing a switch and then a bulb, out of the container?

Calculate the mean, median and mode for the following set of numbers: 0, 1, 1, 2, 3, 5, 8, 13, and 21. It turns out that there is a special name for this number sequence, can you tell us what that is?

Determine the probability of tossing a die and getting a number that is less than 5.

Given the series configuration as displayed in Figure 15.2, if you were given the operating time for each unit as 100 days and the unit failure rate as 2.5 x 10^-4 failures per day, what would be the reliability of the two components in series?

A die is tossed twice. Determine the probability of rolling a 4, 5 or 6, on the first roll; and a 1, 2, 3 or 4 on the second roll.

Consider a core monitoring system for a nuclear reactor with only an ionization chamber (IC), temperature sensor (TS) and pressure sensor (PS). Let us say that the failure probabilities for these subsystems: P(IC) = 0.02; P(TS) = 0.04; and; P(PS) = 0.01; apply Bayes Theorem for determining the probability that the temperature sensor failed during a reactor operation.

A meteorology company is contracted by a solar power plant company that has a solar power plant in both New York City and Los Angeles. The contractor has data which gives the probability of a sunny day in New York City as 0.4, and the probability of a sunny day in Los Angeles as 0.3. The data also show that the probability of a sunny day in either New York City or Los Angeles is 0.58. What is the probability that it will be a sunny day in both New York City and Los Angeles, on the same day? What is the probability that neither New York City nor Los Angeles has a sunny day on the same day?

An electric power plant is designed to have a reliability of 99%. If each subsystem has a reliability of 60%, how many subsystems must be linked in parallel so that the power plant meets its designed specification?

Determine the probability of getting a 3 or a 6, with the toss of a single die.

The probability that a particular man and a particular woman will be alive in another 20 years is 0.8 for the man and 0.9 for the woman. Calculate the probability that both the man and the woman will be alive in 20 years. Also, calculate the probability that neither the man nor the woman will be alive in 20 years. Finally, calculate the probability that either the man or the woman will be alive in 20 years.

A thermal solar power plant consists of 6 subsystems. Each subsystem has a MTTF of 8 months. What is the probability that 1 or 2 failures occur in a 4 month period of operation?

A storage canister has 5 resistors and 4 capacitors. An electrician pulls out two items, consecutively from the canister. The second item is a capacitor. Determine the probability that the first item pulled out of the canister was also a capacitor.

What is the reliability of a simple 2 part system, whose subsystems are connected in series, if each system is in operation for 200 hours and the subsystem failure rate is 2.5 x 10^-4 failures per hour?