Probability Questions

Suppose a diagnostic test for a certain disease has a 95% sensitivity and 90% specificity. It means that the test correctly identifies 95% of people with the disease and correctly identifies 90% of people without the disease. If the prevalence of the disease in a population is 1%, what is the probability that a person who tests positive actually has the disease?

If the time to complete a task is exponentially distributed with a mean of 20 minutes, what is the probability that the task takes less than 10 minutes?

The time until a radioactive particle decays is modeled by an exponential distribution. If the average decay time is 10 seconds, what is the median decay time?

In a dataset of customer purchase history, what kind of analysis would likely involve using joint and conditional probability distributions?

A bag contains 5 red balls and 3 blue balls. Two balls are drawn randomly without replacement. What is the probability that the second ball drawn is red, given that the first ball drawn was blue?

In a normal distribution, what percentage of data falls within three standard deviations of the mean?

Events A and B are independent. The probability of event A is 0.3. The probability of event B is 0.6. What is the probability of both A and B occurring?

A company wants to analyze its website traffic. The time a user spends on the website follows a gamma distribution. Which of these is NOT a suitable use of the gamma distribution in this scenario?

You're a data scientist analyzing website traffic. You have data on the average time users spend on a page, which is 2 minutes with a standard deviation of 30 seconds. You want to estimate the probability that the average time spent on the page by a random sample of 100 users is between 1 minute 55 seconds and 2 minutes 5 seconds. What concept would be most suitable for this calculation?

A fair coin is flipped three times. What is the probability of getting at least two heads?