Hi expert please answer all the questions using your precious time they are from single part , will do like immediately. Thank you
Ill. Slice and Dice 1. You roll a die six times. For each event, choose one of the options. (a) - + - (b)- x- (c) something else a) The first roll is a 1 and the last roll is a 1. b) The first roll is a 1 or the last roll is a 1. N 2. You roll two dice; one is black and the other is white. Find the chance that.. a) Both will land on 5: b) Neither will land on 5: c) The black will land on 5 but not the white: d) The white will land on 5 but not the black: e) One will land on 5 but not the other: f) At least one will land on 5: 3. If you roll a pair of dice, what are the chances they are both 1? Both 2? 4. If you roll a pair of dice and both give the same number, then you "rolled doubles." What are the chances of rolling doubles? 5. In the board game Monopoly, you roll two dice on your turn. If you roll doubles, you get another turn. If you roll doubles again, you get a third turn. If you roll doubles on your third turn, you "go to jail" and have to move your game piece to the "jail" space. What are the chances of going to jail on your turn? (Ignore the other ways you might go to jail.) 6. If you roll two dice, the probability that one of the dice is a 3 and the other is not a 3 is: - x- + 2 x = . Explain the calculation with words. 7. + In Yahtzee, you roll five dice at the same time. If all five dice display the same number, you get to yell "Yahtzee!" and get 50 points. What are the chances you get to yell "Yahtzee!" after a roll? 8. You roll three dice and want to get a 6 on at least one of them. (a) Are the chances of this happening more than, less than, or equal to -? (b) Are the chances of this happening more than, less than, or equal to: = + = + = ? 9. (The Paradox of the Chevalier de Mere). In a gambling game, players bet on the event that in 4 rolls of a die, a 1 (called an "ace" here) would occur at least once. In another game, players bet on the event that in 24 rolls of a pair of dice, a double ace (that is, a 1 on both dice at the same time) would occur at least once. A French nobleman, the Chevalier de Mere, believed that both events had the same chances. He reasoned: * If I have a = chance of getting an ace on one roll, then in 4 rolls I have a 4x-=- chance of getting an ace at least once. * If I have a = chance of getting a double ace on one roll of a pair of dice, then in 24 rolls I have a 24x-==chance of getting a double ace at least once. However, the gamblers found that the first event was a bit more likely than the second. What is wrong with the Chevalier's reasoning? 10. If you roll three dice, what are the chances exactly one of them will be a 6