MCQ Subject: Probability & Statistics

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?

A discrete random variable X can take values 1, 2, or 3 with probabilities 0.2, 0.3, and 0.5 respectively. What is the expected value E(X)?

Two events A and B are defined such that the probability of A occurring does not change based on whether B has occurred. Which of the following best describes their relationship?

In probability theory, which of the following statements about two events A and B is necessarily true if they are mutually exclusive?

A six-sided die is rolled twice. Given that the sum of the two rolls is 7, what is the probability the first roll was a 4?

A fair coin is tossed three times. Given that at least one head appears, what is the probability that all three tosses result in heads?

A discrete random variable X follows a distribution where P(X=1) = 0.4 and P(X=2) = 0.6. Given X is not 2, what is P(X=1)?

A medical test for a disease with 1% prevalence has 90% sensitivity and 95% specificity. What is the probability a person testing positive actually has the disease?

A random variable X follows a distribution where the mean equals the median, and the variance is the square of the standard deviation. Which property does this distribution most likely exhibit?