Question Bank: Probability

What is the probability of getting at least two heads when tossing three fair coins?

In an experiment of rolling a fair die, what is the probability of rolling a number greater than 4?

If event A occurs with probability 0.6 and event B is independent of A with a probability of 0.5, what is the probability of both A and B occurring?

What is the probability that a randomly selected card from a standard deck is a spade or a heart?

What is the conditional probability P(A|B) if P(A) = 0.2, P(B) = 0.4, and P(A ∩ B) = 0.1?

If two events A and B are mutually exclusive, what is the probability of A and B occurring together?

When flipping two coins, what is the probability that at least one coin shows tails?

A box contains 3 red and 2 green balls. What is the probability of picking a green ball?

What is the probability of NOT rolling a number greater than 3 on a fair die?

In a random experiment, if P(A) = 0.3 and P(B) = 0.6, what is P(A or B) if A and B are independent?

If a card is drawn from a deck, what is the probability that it is a face card?

Given the probabilities P(A) = 0.4, P(B) = 0.5, and P(A ∩ B) = 0.1, what is P(A|B)?

In a bag containing 5 white and 5 black balls, what is the probability of drawing one white and one black ball in succession without replacement?

What is the probability of getting a sum of 8 when rolling two six-sided dice?

If a box contains 4 red, 3 blue, and 2 green balls, what is the probability of drawing a red ball first and then a blue ball second, replacing the first?

What does the notation P(E ∩ F) represent?

If P(E) = 0.5 and P(F|E) = 0.2, what is P(E ∩ F)?

In an experiment, if A and B are independent events, which equation holds true?

What is the probability of drawing two black balls from an urn containing 10 black and 5 white balls without replacement?

If P(A) = 0.4 and P(B) = 0.5, what is P(A ∩ B) when A and B are independent?

In a roll of a die twice, what is the probability that both rolls are even numbers?

Three cards are drawn from a pack of 52 cards. What is the probability that the first two are kings and the third is an ace?

If P(E) = 0.3 and P(F) = 0.6, what is P(E ∩ F) when events E and F are not independent?

For two events E and F, if P(E) = 0.1 and P(E ∪ F) = 0.6, what must be true about P(F)?

What is the probability of drawing two aces consecutively from a standard deck without replacement?

If two events are mutually exclusive, which is true about their intersection?

What does the outcome P(E ∩ F) imply if both events have zero probability?

When extending the multiplication rule to three events, what is the correct form?

What is the formula for calculating conditional probability P(E|F)?

If P(A) = 0.3 and P(B) = 0.5, what is P(A|B) if A and B are independent?

In a card game, what is the probability of drawing a heart given that a red card has been drawn?

What is the conditional probability of event A given event B when P(A ∩ B) = 0.1 and P(B) = 0.25?

If P(A) = 0.6 and P(B|A) = 0.4, what is P(A ∩ B)?

What is P(A ∪ B | C) if P(A|C) = 0.5, P(B|C) = 0.2, and P(A ∩ B|C) = 0.1?

If two events are independent, what can we say about P(A ∩ B)?

In a family with two children, what is the conditional probability both are girls given that at least one is a girl?

What is the probability of getting a sum of 4 when rolling two dice?

If a die is rolled, what is the conditional probability of rolling a 1 given that an odd number has been rolled?

What is the conditional probability that event A occurs given that event B occurs, if P(A) = 0.3, P(B) = 0.6, and P(A ∩ B) = 0.2?

What is the conditional probability of obtaining a 3 on a die given that the roll is odd?

Two coins are tossed, what is the conditional probability of getting at least one head given that at least one tail is obtained?

If the probability of event A occurring is 0.4 and the probability of event A given event B is 0.5, what can be deduced about events A and B?

If P(A) = 0.8 and P(A|B) = 0.6, what is P(B) if A and B are independent?

If a test for a disease is 90% accurate, what is the probability that a person has the disease if they test positive, given that the overall disease prevalence is 0.1%?

If two events A and B are independent, which of the following represents the probability of both events occurring?

A factory produces three types of bolts with different rates of defects. If a bolt is found to be defective, what is the probability it was made by machine B?

A fair coin and an unbiased die are tossed. Let A be the event ‘head appears on the coin’ and B be the event ‘3 on the die’. Are A and B independent?

A doctor arrives late to an appointment. If the transport methods are varied, what is the probability he came by train?

If P(A) = 0.4 and P(B) = 0.5 for independent events A and B, what is P(A ∩ B)?

A man speaks the truth 75% of the time. If he claims he rolled a six on a die, what is the probability it is actually a six?

Given that P(A) = 1/2 and P(B) = 1/3 for independent events A and B, what is P(A ∪ B)?

How do we obtain the probability of an event given a positive test result under Bayes' Theorem?

Which of the following pairs of events is independent?

If the probability of testing positive for a disease when one is actually sick is 0.95, but when one is not sick it is 0.1, what can be inferred using Bayes' Theorem?

What does it mean for events E and F to be independent?

What is Bayes' Theorem primarily used for?

If P(A) = 0.6 and P(B) = 0.4, and they are independent, what is P(B')?

In a scenario with two drugs, Drug A has 85% accuracy, while Drug B has 75%, what is crucial to consider with Bayes' Theorem?

Two dice are rolled. If A is the event that at least one die shows a 6 and B is the event that the sum is greater than 8, are A and B independent?

Given two events A and B, if A is a subset of B, how does Bayes' Theorem apply?

If the probability of event A occurring is 0.7 and the probability of event B occurring is 0.3, what is P(A ∩ B) if A and B are independent?

If you draw a card from a standard deck, what is the probability that it is a heart given that it is red?

Let E and F be events such that P(E) = 0.5 and P(E ∩ F) = 0.2. Are E and F independent?

In Bayesian analysis, what does the prior probability represent?

What is the probability of the complement of event A if A is independent with P(A) = 0.2?

What is the error in directly applying Bayes' Theorem without accounting for P(E)?

If two events E and F are such that P(E) = 1/4, P(F) = 1/2, and P(E ∩ F) = 1/8, are these events independent?

If event C occurs given events A and B, how can Bayes' Theorem be applied?

A box contains 3 red balls and 2 blue balls. If you draw two balls with replacement, what is the probability that both are red?

Which probability distribution is often connected with Bayes' Theorem?

What is the probability of getting at least one head when tossing two independent coins?

For two events A and B that are independent, how does it affect their Bayes' probabilities?

How does Bayes' Theorem refine initial probabilities based on new data?