A magician performs the following card trick. She asks a volunteer to secretly select a number between 1 and 10 and deal out that many cards from a well-shuffled deck of52 standard playing cards. The last card dealt determines a new number of cards to be dealt from those remaining: if it is an ace, the new number is 1; if it is Jack, Queen orKing, the new number is 5; otherwise the new number is the face value of the card.The process is repeated until there are not enough cards left in the deck to continue.The magician then identifies the last card selected.

The trick is that the magician repeats the process starting with the number 1. This will usually (but not always) result in selecting the correct final card, no matter what number the volunteer originally selected

a) Perform an experiment to estimate the probability the magician and the volunteer end up with the same final card. Give full details of the experimental 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 card, no matter what number the volunteer chooses initially.