Could you help me with 6 a c and d please. I am having trouble with this question.

STA1010 Statistical M Question 6 [8 Marks] A magician performs the following card trick. She asks a volunteer to secretly select a number between 1 and 13 and deal that number of cards from a well-shuffled face- down pile of 52 standard playing cards to form a face-up pile. The last card dealt determines a new number of additional cards to be dealt from the face-down pile to the face-up pile: if it is an ace, the new number is 1; if it is Jack, Queen or King, the new number is 11, 12 or 13 respectively; otherwise the new number is the face value of the card. This process is continued: at each stage, the last card dealt determines the new number of cards to deal from the face-down pile to the face-up pile. The process ends when the new number to be dealt is larger than the number of cards left in the face-down pile. The volunteer remembers that last number (the number that was too large) and deals any remaining cards from the face-down pile onto the face-up pile. All this is done with the magician out of the room. The magician then enters the room, turns the pile of face-up cards face-down without shuffling and repeats the process, but starting with the number 1 (which may or may not be the initial number chosen by the volunteer). When the trick works, the magician gets the same last number as the volunteer, no matter what number the volunteer started with. But the trick doesn't always work! a) Perform an experiment to estimate the probability the magician and the volunteer end up with the same last number. Give full details of the experiment and result. You may pool results with other students. (Keep your results - you will need them again for Assignment 2!) b) What is the population you are sampling in this experiment? c) Explain why the magician and volunteer are likely to end up with the same last number, no matter what number the volunteer chooses initially. d) If the trick is performed with two decks of 52 cards shuffled together, is it more or less likely to work? Justify your answer. tv APR 6 A W P X