Solution:
Given that
A denote the riffle shuffle which interleaves the top half of the deck with the bottom half,but keeps the top and bottom cards fixed.
B denote the other kind of riffle( in which all cards move)
3. For a deck consisting of 32 playing cards, let A denote the riffle shuffle which interleaves t...
If you take a deck of 2n playing cards, cut it into two stacks of n and interleave them, you have performed a perfect shuffle. Example: for the six-card deck [1 2 3 4 5 6]T , the result is [4 1 5 2 6 3]T (note that the top card of the second stack goes on top. Write down the matrix A2n for a perfect shuffle of 2n cards when 2n=10 and 2n=12. How many times must you (perfectly)...
If you take a deck of 2n playing cards, cut it into two stacks of n and interleave them, you have performed a perfect shuffle. Example: for the six-card deck [1 2 3 4 5 6]T , the result is [4 1 5 2 6 3]T (note that the top card of the second stack goes on top. Write down the matrix A2n for a perfect shuffle of 2n cards when 2n=10 and 2n=12. How many times must you (perfectly)...
13. [3] You shuffle a deck of playing cards and the chance you get a diamond card is 0.25. You repeat this process 200 times, putting the card back each time, and out of those 200 attempts you get 57 diamond cards. This demonstrates a. The law of large numbers b. The law of averages 14. [3] You shuffle a deck of playing cards and the chance you get a diamond card is 0.25. You repeat this process times, putting...
A random experiment consists of drawing a card from an ordinary deck of 52 playing cards. Let the probability set function P assign a probability of 1 52 to each of the 52 possible outcomes. Let C1 denote the collection of the red cards (hearts and diamonds) and let C2 denote the collection of the 4 kings plus the 4 aces. Compute P(C1), P(C2), P(C1 ∩C2), and P(C1 ∪C2).
5 cards are drawn from a standard deck of 52 playing cards. How many different 5-card hands are possible if the drawing is done without replacement?
2. Consider a standard 52 card deck of playing cards. In total there are four cards that are Aces, four cards that are Kings, four cards that are Queens and four cards that are Jacks. The remaining 36 cards are four each of the numbers 2, 310. That is there are four cards that are twos, four cards that are threes etc. For this question, suppose that we reduce the number of cards in the deck by removing one of...
Consider a standard 52-card deck of cards. In particular (for those unfamiliar with playing cards), the deck contains 4 aces, 4 kings, 4 queens, 4 Jacks, 4 10's, 4 94, 4 84, 4 7's, 4 6's, 4 5's, 4 4's, 4 3, and 4 2's, where for each type of card (for example ace), one of the 4 copies is of suit club, one is of suit heart, one is of suit spade, and one is of suit diamond. Consider...
You shuffle a deck of 52 cards well and then expose the top 3 cards. Give exact answers expressed as simplified fractions. (a) What is the probability that the 3 cards are from 3 different suits? Use the sample space consisting of ordered triples (x1, x2, x3), where xi is the i-th card exposed. (b) What is the probability that the 3 cards are from 3 different suits? Use the sample space consisting of sets {x1, x2, x3} of 3...
7. There are 52 playing cards; let S be the set of all of them. A "deck" is a particular order (or permutation) of the 52 cards. Mathematically, a deck can be represented by (ci,, 2) where ci,c2,., cs2 are all the elements of S. The interpretation is that ci is the first card in the deck, c2 is the second card, and so on. Let 2 be the set of all possible decks. a) Is Ω a subset of...
CS102 : JAVA Object-Oriented Programming.
1 Write a class Card whose instances represent a single playing card from a deck of cards. Playing cards have two distinguishing properties an integer for the rank (1 (corresponding to Ace) ,2,3, 13 (correspond ing to King) and suit (Spades, Hearts, Diamonds, or Clubs). Make the suit an enumerated data type. Include getters and setters and a method that tests if a card is valid. Write a class named Deck whose instances are full...