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1.) A card is selected from a standard deck of 52 playing cards. A standard deck of cards has 12 face cards and four Aces (Aces are not face cards). Find the probability of selecting · a three given the card is a not a face card. Given that the card is not a face card, there are 40 non-face cards and 4 threes. The probability that the card is a three is 4/40 = 1/10 = 0.10 · a four, given that the card is not a diamond. Given that the card is not a diamond, there are 39 non-diamond cards. There are only 3 fours remaining, since the 4 of diamonds is excluded. The probability that the card is a four is 3/39 = 1/13 · a Jack given the card is not a face card. Since it is given that the card is not a face card, and since a Jack IS a face card, the probability that the card is Jack is 0. Show step by step work. Give all solutions exactly in reduced fraction form. 2.) A mini license plate for a toy car must consist of three numbers followed by a letter. Each number must be a 1, 3, or 5. Repetition of digits is NOT permitted. Each letter must be an A, B or C. *Use the counting principle to determine the number of points in the sample space. There are 3 choices for the first number, 2 choices for the second number, 1 choice for the third number, and three choices for the letter. The total number of combinations is then: 3 * 2 * 1 * 3 = 18 *Construct a tree diagram to represent this situation *List the sample space. 135A 135B 135C 153A 153B 153C 315A 315B 315C 351A 351B 351C 513A 513B 513C 531A 531B 531C *Determine the exact probability of creating a mini license plate with a C. Give solution exactly in reduced fraction form. There are 6 plates that contain a C, and a total of 18 plates. The probability of a plate having a C is 6/18 = 1/3 3.) A bag contains 6 purple marbles, 7 azure marbles and 10 orange marbles. What is the chance of drawing an orange marble? If an orange marble is drawn then placed back into the bag, and a second marble is drawn, what is the probability of drawing an azure marble? Give solutions exactly in reduced fraction form, separated by a comma. There are a total of 6 + 7 + 10 = 23 marbles. The probability of drawing an orange marble is 10/23. The probability of drawing an azure marble is 7/23.