4. (10 points) Consider the following technique for shuffling a deck of n cards: For any initial ordering of the cards,

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4 10 Points Consider The Following Technique For Shuffling A Deck Of N Cards For Any Initial Ordering Of The Cards 1 (29.8 KiB) Viewed 85 times

4. (10 points) Consider the following technique for shuffling a deck of n cards: For any initial ordering of the cards, go though the deck one card at a time and at each card, flip a coin with probability p of getting a head. If the coin comes up heads, then leave the card where it is; if the coin comes up tails, then move that card to the end of the deck. After the coin has been flipped n times, say that one round has been completed. For instance, if n = 4 and the initial ordering is 1,2,3,4, then if the successive flips result in the outcome H, T, T, H, then the ordering at the end of the round is 1,4, 2, 3. (a) What is the probability that the ordering after one round is the same as the initial ordering? (b) If the coin is a fair coin (p=0.5), what will be the numerical value of the probability in (a)?