Please answer all shown parts of each question and show detailed work along with explanations, thanks!

i. A normal deck of cards has 52 cards, consisting of 13 each of four suits: spades, hearts, diamonds, and clubs. Hearts and diamonds are red, while spades and clubs are black. Each suit has an ace, nine cards numbered 2 through 10, and three face cards. The face cards are a jack, a queen, and a king. Answer the following questions for a single card drawn at random from a wellshufed deck of cards. (I. What is the probability of drawing a red card? What is the probability of drawing an ace? What is the probability of drawing a red ace? Are these events (\"ace\" and \"red\") mutually exclusive? Are they independent? W f. What is the probability of drawing a red king? What is the probability of drawing a face card in hearts? Are these two events mutually exclusive? Are they independent? '. A ycatcher is trying to catch passing bugs. The probability that it catches a bug on any given try is 20%. a. What is the probability that it catches its first bug on its fourth try? b. What is the probability that at least four failures occur before the ycatcher has its rst success