Sarah picks 2 cards from a thoroughly shuffled deck of cards and examines them 1. Which...
1) You start with a full deck of cards, which have been shuffled. You draw cards from the deck, with out replacement, until you get a card other than an ace. What is the expected value of the number of cards drawn? 2) What is the expected number of face cards (jack, queen, or king) in a three card hand drawn at random from a standard deck of cards?
1) You start with a full deck of cards, which have...
Suppose a standard deck of 52 playing cards is thoroughly shuffled and a single card is drawn. Suppose an ace has value 1, a jack has value 11, a queen has value 12, and a king has value 13. (a) Compute P(X = x) for every real number x, when X is the value of the card drawn. (b) Suppose that Y = 1, 2, 3, or 4 when a diamond, heart, club, or spade is drawn. Compute P(Y =...
Describe a sample space for successively drawing and keeping 4 cards from a standard deck of 52 cards if we record the value and suit of each card. Find the probability of each of the following: a. Ace, King, Queen, Jack of spades in that order; b. Ace, King, Queen, Jack of spades in any order; c. Ace, King, Queen, Jack: any suit, any order; d. all 4 selected cards are red; e. the cards selected are 3 hearts and...
you are dealt 2 cards successively (without replacement) from a shuffled deck of 52 playing cards. Find the probability that the first card is a king and the second card is a queen.
(12 pts) 3. a Draw 10 cards at random and with replacement from a standard deck of cards. What is the probability that at most 2 of them are face cards? (A face card is a Jack, Queen, or King.) Suppose you deal 10 cards, without replacement, off the top of a well-shuffled deck. What is the probability that they are all hearts? In this problem, assume that the gender of any child that a couple has is equally likely...
The following exercise refers to choosing two cards from a thoroughly shuffled deck. Assume that the deck is shuffled after a card is returned to the deck. If you put the first card back in the deck before you draw the next, what is the probability that the first card is a club and the second card is a spade? (Enter your probability as a fraction.)
The following exercise refers to choosing two cards from a thoroughly shuffled deck. Assume that the deck is shuffled after a card is returned to the deck. If you put the first card back in the deck before you draw the next, what is the probability that the first card is a 7 and the second card is a ace?
1. A standard deck of cards has 52 cards with 4 suits that include 13 clubs, 13 diamonds, 13 hearts, and 13 spades. Each suit includes an ace, a king, a queen, and a jack, and numbers 2 through 10. Assume that I choose one card from the deck. a. What is the probability that the card is either a queen or a 4? b. What is the probability that the card is not a queen and it is not...
2. (10 points) Suppose you are playing blackjack against a dealer. In a freshly shuffled deck, what is the probability that either you or the dealer is dealt a blackjack? (Recall the game of blackjack is played with each player obtaining two cards at random from a regular deck. We say these two cards form a blackjack if one card is an ace and the other card is either a 10, Jack, Queen or King)
2. (10 points) Suppose you...
4 cards are randomly drawn from a standard deck of playing cards. What is the prob- ability that all their suits are different? Hint: There are 52 cards in a standard deck of playing cards. A card can have 4 different suits: diamond ( ♦ ), club ( ♣ ), heart ( ♥ ), or spades ( ♠ ). There are 13 cards of each suit. Cards are further labeled by their rank: numbers 1 to 10 and three face...