The following problem involves a standard deck of 52 playing cards. In such a deck of cards there are four suits of 13 cards each. The four suits are: hearts, diamonds, clubs, and spades. The 26 cards included in hearts and diamonds are red, The 26 cards include clubs and spades are black. The 13 cards in each suit are: 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, and Ace. This means there are four Aces, four Kings, four Queens, four 10s, etc., down to four 2s in each deck. You draw two cards from 3 standard deck of 52 cards, but before you draw the second card, you put the first one back and reshuffle the deck, (a) Are the outcomes on the two cards independent? why? o, The events cannot occur together. ves. The events can occur together. 'Yes. The probability of drawing a specific second card is the same regardless of the identity of the first drawn card, Na. The probability of drawing a specific second card depends on the identity of the first card. (b) Find A(Ace on 1% card and 9 on 2"), (Enter your answer as a fraction.) (c) Find (9 on 1% card and Ace on 2"9), (Enter your answer as a fraction.) (d) Find the probability of drawing an Ace and a 9 in either order. (Enter your answer as a fraction.) A sales representative must visit eight cities. There are direct air connections between each of the cities. Use the multiplication rule of counting to determine the number of different choices the sales representative has for the order in which to visit the cities.In the Cash Now lottery game there are 7 finalists who submitted entry tickets on time, From these 7 tickets, three grand prize winners will be drawn. The first prize is one million dollars, the secand prize is ane hundred thousand dollars, and the third prize is ten thousand dollars, Determine the total number of different ways in which the winners can be drawn, (Assume that the tickets are not replaced after they are drawn.) You roll two fair six-sided dice, a green one and a red one. (a) What is the probability of getting a sum of 3? (Enter your answer as a fraction.) (b) What is the probability of getting a sum of 9? (Enter your answer as a fraction.) (c) What is the probability of getting a sum of 3 or 9? (Enter your answer as a fraction.) Are these outcomes mutually exclusive? O Yes O NoIn the Cash Now lottery game there are 7 finalists who submitted entry tickets on time, From these 7 tickets, three grand prize winners will be drawn. The first prize is one million dollars, the secand prize is ane hundred thousand dollars, and the third prize is ten thousand dollars, Determine the total number of different ways in which the winners can be drawn, (Assume that the tickets are not replaced after they are drawn.) In the Cash Now lottery game there are 7 finalists who submitted entry tickets on time, From these 7 tickets, three grand prize winners will be drawn. The first prize is one million dollars, the secand prize is ane hundred thousand dollars, and the third prize is ten thousand dollars, Determine the total number of different ways in which the winners can be drawn, (Assume that the tickets are not replaced after they are drawn.)