You and three friends are playing games with a well-shuffledstandard deck of 52
ID: 2914252 • Letter: Y
Question
You and three friends are playing games with a well-shuffledstandard deck of 52 cards and four fair, six-sided dice. (a) In the first game, you are dealt thefirst five cards off of the top of the deck of cards (drawn wothoutreplacement). What is the probability that you receive, in order,the ace of spades, the 10 of diamonds, the 5 of hearts, the 2 ofclubs and the jack of spades? (b) For the second game you roll the fourdice together and calculate the sum. What is the probability thatthe sum is greater than 21? (c) You re-shuffle the deck and play a thirdgame. In this game, players take turns drawing one card (withoutreplacement) from the deck and rolling one die. A pleayerautomatically wins if that player draws and ace and rolls a six ordraws a two and rolls a one. What is the probability of the firstplayer automatically winning? (d) The first player didn't automaticallywin, since he drew an ace but rolled a four. What is theprobability of the second player automatically winning? (e) In the fourt game, you re-shuffle thedeck and deal 13 cards to each of the four players. What is theprobability of dealing all of the spades to the first player? You and three friends are playing games with a well-shuffledstandard deck of 52 cards and four fair, six-sided dice. (a) In the first game, you are dealt thefirst five cards off of the top of the deck of cards (drawn wothoutreplacement). What is the probability that you receive, in order,the ace of spades, the 10 of diamonds, the 5 of hearts, the 2 ofclubs and the jack of spades? (b) For the second game you roll the fourdice together and calculate the sum. What is the probability thatthe sum is greater than 21? (c) You re-shuffle the deck and play a thirdgame. In this game, players take turns drawing one card (withoutreplacement) from the deck and rolling one die. A pleayerautomatically wins if that player draws and ace and rolls a six ordraws a two and rolls a one. What is the probability of the firstplayer automatically winning? (d) The first player didn't automaticallywin, since he drew an ace but rolled a four. What is theprobability of the second player automatically winning? (e) In the fourt game, you re-shuffle thedeck and deal 13 cards to each of the four players. What is theprobability of dealing all of the spades to the first player?Explanation / Answer
(a) In the first game, you are dealt thefirst five cards off of the top of the deck of cards (drawn withoutreplacement). the probability that you receive, in order, the ace of spades,the 10 of diamonds, the 5 of hearts, the 2 of clubs and the jack ofspades = (1/52) x (1/51) x (1/50) x (1/49) x (1/48) (b) For the second game you roll the fourdice together and calculate the sum. the sum canbe greater than 21 if the cases are (6,6,6,4) , (5,5,6,6),(5,6,6,6), (6,6,6,6) the probability of getting the above =4x(1/6)x(1/6)x(1/6)x(1/6) = 0.0031 (c) You re-shuffle the deck and play a thirdgame. In this game, players take turns drawing one card (withoutreplacement) from the deck and rolling one die. A pleayerautomatically wins if that player draws an ace and rolls a six ordraws a two and rolls a one. the probability of the first playerautomatically winning = (4/52) x(1/6) +(4/52)x(1/6) =0.2564 (d) The first player didn't automaticallywin, since he drew an ace but rolled a four. the probability of thesecond player automatically winning= (3/51)x(1/6) +(4/ 51)x(1/6) = 0.0229 (e) In the fourth game, you re-shuffle thedeck and deal 13 cards to each of the four players. What is theprobability of dealing all of the spades to the first player= (13!)/(52!)Related Questions
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