Question

2. Bob flips a coin 3 times.

Let A be the event that Bob flips Heads on the first two flips.

Let B be the event that Bob flips Tails on the third flip.

Let C be the event that Bob flips Heads an odd number of times.

Let D be the event that Bob flips Heads at least one time.

Let E be the event that Bob flips Tails at least one time.

(a) Determine whether A and B are independent.

(b) Determine whether A and C are independent. (When computing P(C) don’t forget to account for orderings!)

(c) Determine whether A, B, and C are independent.

(d) Determine whether A and D are independent.

(e) Determine whether D and E are independent.

HINT: In this problem justify your answer by computing the appropriate probabilities. Recall that events F and G are independent if P(F G) = P(F)P(G).

Answer 1