MCQ Subject: Probability & Statistics

A bag contains 5 red and 3 blue balls. If 2 balls are drawn at random without replacement, what is the probability the second ball is red given the first ball drawn was red?

A diagnostic test for a disease has a 95% detection rate among those with the disease and a 5% false-positive rate among those without it. If 1% of the population actually has the disease, what is the probability that a person testing positive actually has the disease?

Which continuous probability distribution is characterized by the property that the future lifetime of a component is independent of its current age?

A disease with 1% prevalence has a diagnostic test with 95% sensitivity and 95% specificity. If someone tests positive, what is the approximate probability they actually have the disease?

Which probability distribution is commonly used to model the number of successes in a fixed number of independent Bernoulli trials?

A diagnostic test for a disease has 95% sensitivity and specificity. If 1% of the population has the disease, what is the probability a person testing positive actually has the disease?

In a sampling distribution of the sample mean, how does the variance change as the sample size increases?

Two independent components each have a probability of 0.9 of working properly. What is the probability that both components work simultaneously?

In a factory, 60% of the workers are males, and 40% are females. It is known that 20% of males and 30% of females are absent on any given day. If a worker is absent today, what is the probability that the worker is female?

Two independent coins are tossed. Given that at least one head appears, what is the probability that both are heads?