A university registrar is analyzing student enrollment data for two popular elective courses: Introduction to Robotics (R) and Advanced Python Programming (P). You are given the following information:

• 10% of students are not enrolled in either Robotics or Python Programming.
• 75% of those students who are enrolled in at least one of these courses are enrolled in Introduction to Robotics.
• 40% of those students who are enrolled in at least one of these courses are enrolled in Advanced Python Programming.

Determine the probability that a randomly selected student at the university is enrolled in Advanced Python Programming but not Introduction to Robotics.

• 0.195
• 0.210
• 0.225
• 0.240
• 0.255

The reliability of a car's automatic transmission is a critical factor for owners. For a specific luxury sedan model, studies on transmission longevity have yielded the following probabilities:

• The probability that the transmission will require a major repair before reaching 50,000 miles is [math]0.1[/math]
• The probability that the transmission will require a major repair before reaching 100,000 miles is [math]0.5[/math]
• The probability that the transmission will require a major repair before reaching 150,000 miles is [math]0.8[/math]

You own one of these luxury sedans, and it has reliably accumulated exactly 100,000 miles without any transmission issues. What is the probability that its automatic transmission will require a major repair in the next 50,000 miles (i.e., before the car reaches 150,000 miles)?

• 0.4
• 0.5
• 0.6
• 0.7
• 0.8

One coin in a collection of 65 has two heads. The rest are fair. If a coin, chosen at random from the lot and then tossed, turns up heads 6 times in a row, what is the probability that it is the two-headed coin?

• 0.4
• 0.45
• 0.5
• 0.55
• 0.6

References

Doyle, Peter G. (2006). "Grinstead and Snell's Introduction to Probability" (PDF). Retrieved June 6, 2024.

A blood test indicates the presence of a particular disease 95% of the time when the disease is actually present. The same test indicates the presence of the disease 0.5% of the time when the disease is not actually present. One percent of the population actually has the disease.

Calculate the probability that a person actually has the disease given that the test indicates the presence of the disease.

• 0.324
• 0.657
• 0.945
• 0.950
• 0.995

(Chung^{[Notes 1]}) In London, half of the days have some rain. The weather forecaster is correct 2/3 of the time, i.e., the probability that it rains, given that she has predicted rain, and the probability that it does not rain, given that she has predicted that it won't rain, are both equal to 2/3. When rain is forecast, Mr. Pickwick takes his umbrella. When rain is not forecast, he takes it with probability 1/3. Find the probability that he brings his umbrella, given that it doesn't rain.

• 2/9
• 1/3
• 5/9
• 2/3
• 7/9

Notes

References

Doyle, Peter G. (2006). "Grinstead and Snell's Introduction to Probability" (PDF). Retrieved June 6, 2024.