Please show all work and the logic behind every number used

(8] We toss a fair coin 9 times, observing heads or tails each time. Let E be the event that heads appears at least 5 times, and let F be the event that tails appears at least 3 times. (a) Find the total number of possible outcomes. (b) Find the probability that tails appears at least 3 times if we know that heads ap pears at least 5 times by completing the following and carrying out the computation: P{_|_) = . . . (place E and F in the appropriate blanks, then do the calculation]. A relevant example: If we want to know the number of ways to get exactly 7 heads amongst the 9 tosses, it would be [El Imagine our 9 tosses are a sequence of blanks to be lled in with Hs and Ts _________ . The number (3) tells us how many ways there are to select 7 blanks to be Hs. You can also think of it as an arrangement of 7 He and 2 Ts, which is (9) = (9). as 7