MCQ Subject: Probability & Statistics

60% of components are made by Machine A (2% defective) and 40% by Machine B (5% defective). What’s the probability a defective component comes from Machine A?

A fair coin is tossed three times. Given that at least two tosses resulted in heads, what is the probability that all three tosses were heads?

If two events A and B are independent, and P(A) = 0.4, P(B) = 0.6, what is P(A|B), the probability of A given B?

If the probability of event A occurring is 0.3 and the probability of event B occurring is 0.4, and the probability of both A and B occurring is 0.12, what is the nature of events A and B?

In probability theory, which of the following statements accurately distinguishes between independent and mutually exclusive events?

Which of the following probability distributions is characterized by having a mean equal to its variance?

Two fair dice are rolled simultaneously. What is the probability that the sum of the numbers on both dice is 7, given that at least one die shows a 4?

Which of the following probability distributions is symmetric around its mean?

If the probability of a coin landing on heads is 0.5 and the probability of raining tomorrow is 0.3, what is the probability that the coin lands on heads AND it rains tomorrow?

A disease test is 90% accurate for those with the disease and 80% accurate for those without. If 1% of the population has the disease, what’s the probability of having the disease given a positive test?