Calculate Expected Flips for Two Heads Coin Toss

##### Scenario Experian DataLabs online assessment – core probability section. Several short probability problems are asked back to back, covering coin-flip distributions and conditional probability. ##### Question Answer the following: 1. You repeatedly flip a fair coin until you obtain two heads (not necessarily consecutive). What is the expected number of flips? 2. If you flip a fair coin three times, what is the probability of getting exactly two heads? 3. Given two events A and B with P(A) = 0.3, P(B) = 0.5, and P(A ∩ B) = 0.15, compute P(A | B). 4. Given two events A and B with P(A) = 0.3, P(B) = 0.4, and P(A ∩ B) = 0.12, compute P(A | B). ##### Hints - For waiting-time problems, use the geometric / negative-binomial expectation E[T] = r / p. - For a fixed number of flips, use the binomial PMF P(X = k) = C(n, k) p^k (1 − p)^(n − k). - For conditional probability, apply P(A | B) = P(A ∩ B) / P(B), and check whether the events are independent.