Statistics and Probability Answers

Let A and B be two events. Suppose the probability that at least one of them occurs is 2/3. What
is the probability that neither A nor B occurs?

Which one of the following statements is/are true regarding cohort and case-control studies?

(I) Case-control studies are controlled experiments, whilst cohort studies are observational studies.

(II) Case-control studies are better for rare diseases, compared to cohort studies.

A certain town has a population of 100,000, of which 20,000 are smokers and 80,000 are non-smokers. It is known that for the population, r(lung cancer | smoker) = 5% and r(lung cancer | non-smokers) = 1%. Suppose that 50% of lung cancer patients are chosen by simple random sampling, while 10% of residents without lung cancer are chosen by simple random sampling. By calculating r(lung cancer | smoker) in the sample using expected numbers, what can we say about

U = sample r(lung cancer | smoker) and V = population r(lung cancer | smoker)?

1. U = V
2. U < V
3. U > V

Given that the odds of an event A occurring is 5, what is the risk of event A happening?

I have a fair 12-sided (dodecahedron) die with sides labelled 1, 2, …, 12 respectively. See https://images.app.goo.gl/FGseg31kiTAW7psK6 for an example of a fair 12-sided die. I also have a fair 6-sided die with sides labelled 1, 2, …, 6 respectively. I roll the first die on a table with a standard protocol, then roll the second die on another table also with a standard protocol. What is the probability that the sum of the numbers appearing face up on the two dice is 11?

The following table represent daily wages (in rupees) of the workers in a certain commercial organisation : [5] Daily Wages 200-300 300-400 400-5001500-600 Number of Workers 05 10 03 1 02 Calculate mean and standard deviation of the above data.

The following table gives data for a sample of married women, the level of education and marriage adjustment score : Marriage Adjustment Score Level of Education Low High Very High Middle School 25 5 10 High School 50 30 40 College 120 60 60 Can you conclude from the above, the higher the level of education, the greater is the adjustment in marriage ? Justify. Given that x0.05 (4) = 9.488

The rate at which cars arrive at the garage is 12 cars per hour. If the arrival of cars at the garage is assumed to follow a poisson distribution, 1 what is the probability that in the next hour there will be at at most 1 car arriving at the garage

Although Chung was successful in creating and maintaining a disciplined company culture, OD consultants argue that, it could have been much better if Chung had appointed an outsider to spearhead the changes. Argue for or against the use of using an outsider in spearheading change at the headquarters of Kia Motors America.