Probability and statistics for engineering and the sciences

5. We toss a fair coin twice. Let T1 = {1st toss is a tail}, T2 = {211.1 toss is a tail}, and D = [the two tosses have different results} Calculate the probabilities of events T1, T2, and D: P(T1), P(T2), and P(D) b. Calculate the probability of the event {T1 and T2 take place given that D took place} c. Calculate the probabilities of the events T1/D (T1 given that D took place) and T2/D (T2 given that D took place) 9' Extra CREDIT (5 PTS) d. Are the events T1/D and T2/D in part (c) independent? Explain using the (mathematical) denition of independence