MC: Probability Trees And Conditional Expectations

Question 1

What are independent events?

Answer 1

Independent events are those where the occurrence of one event does not change the probability of another event occurring.

Example: Flipping a fair coin.

Question 2

What is the formula for calculating the probability of event A given event B for independent events?

Answer 2

P(A|B) = P(A)

This means the probability of A remains the same regardless of whether B occurs.

Question 3

Calculate the probability of getting 3 heads when flipping a fair coin.

Answer 3

P(3 heads) = 0.5 × 0.5 × 0.5 = 0.125

This represents the probability of the independent event of getting heads in three consecutive flips.

Question 4

What are dependent events?

Answer 4

Dependent events are those where knowing the outcome of one event changes the probability of another event occurring.

Example: Picking cards from a pack without replacement.

Question 5

What is the formula for calculating the probability of event A given event B for dependent events?

Answer 5

P(A|B) ≠ P(A)

This indicates that the probability of A changes based on whether B has occurred.

Question 6

Calculate the probability of drawing 2 aces from a deck of cards without replacement.

Answer 6

P(2 aces) = (4 / 52) × (3 / 51) = 0.0045

This calculation shows how the probability changes after the first draw.

Question 7

Just a visual on bayes formula

Answer 7