Question

In: Statistics and Probability

Five cards are dealt from a standard 52 card deck Determine the number of possible outcomes...

Five cards are dealt from a standard 52 card deck

  1. Determine the number of possible outcomes we could obtain
  2. What is the probability we draw
    1. Any flush (five cards of same suit)
    2. Four of a kind ( four cards of all the same rank)

Solutions

Expert Solution

a)

Total cards = 52          
number of possible outcomes of selecting 5 cards = 52C5 = 2598960          

b-a)

so, total possible ways of flush = 13C5*4 = 5148
So, P(Flush) = 5148/2598960=0.001980792

b-b)

Four of a kind-   4 cards of one denomination and one card of a second denomination.                  
there is 13 possible cases of one denomination                      
second denomination means 12 possible cases will occur                      
from 12 cases either 1 from a set (4 suit)                      
total number of ways =13C1*12C1*4C1 =   624                  
                      
P(four of a kind) = 624/2598960=   0.000240096                 

orchestra answered 2 years ago
Next > < Previous

Related Solutions

A five-card poker hand dealt from a standard 52-card deck of playing cards is called a...
A five-card poker hand dealt from a standard 52-card deck of playing cards is called a three-of-a-kind hand if it contains exactly three cards of the same rank (e.g. 3 aces and 2 other cards). How many distinct three-of-a-kind hands can be dealt with? Calculate a numeric answer.
In a standard deck of 52 cards。 (a) What are the total number of five card...
In a standard deck of 52 cards。 (a) What are the total number of five card hands? (b) What is the probability of having exactly two Aces? (c) What is the probability of getting a hand containing five Two’s? (d) What is the probability of a Three given that the first four cards are not a Three?
You are dealt a hand of five cards from a standard deck of 52 playing cards....
You are dealt a hand of five cards from a standard deck of 52 playing cards. Calculate the probability of the given type of hand. (None of them is a recognized poker hand.) (a) Mixed royal meeting: One of each type or royal card (king, queen, jack, ace) of different suites, and a last non-royal card (neither king, queen, jack or ace). Enter a formula. Examples: C(5,3)C(33,3)/C(14,2) C(5,3)C(33,3)C(4,1)/C(100,100) (b) Red and black double royal wedding: A red king, a red...
You are dealt a hand of five cards from a standard deck of 52 playing cards....
You are dealt a hand of five cards from a standard deck of 52 playing cards. Calculate the probability of the given type of hand. (None of them is a recognized poker hand.) 1. Double royal interracial wedding: Two kings of one color, two queens of the other color, and a last non-royal card (neither king, queen, jack or ace). Solve using a formula. Examples:  C(5,3)C(33,3)/C(14,2) or C(5,3)C(33,3)C(4,1)/C(100,100)
A poker hand consists of five cards randomly dealt from a standard deck of 52 cards....
A poker hand consists of five cards randomly dealt from a standard deck of 52 cards. The order of the cards does not matter. Determine the following probabilities for a 5-card poker hand. Write your answers in percent form, rounded to 4 decimal places. Determine the probability that exactly 3 of these cards are Aces. Answer:  % Determine the probability that all five of these cards are Spades. Answer:  % Determine the probability that exactly 3 of these cards are face cards....
A poker hand consists of five cards randomly dealt from a standard deck of 52 cards....
A poker hand consists of five cards randomly dealt from a standard deck of 52 cards. The order of the cards does not matter. Determine the following probabilities for a 5-card poker hand. Write your answers in percent form, rounded to 4 decimal places. Determine the probability that exactly 3 of these cards are Aces. Answer: % Determine the probability that all five of these cards are Spades. Answer: % Determine the probability that exactly 3 of these cards are...
A) A poker hand consists of five cards randomly dealt from a standard deck of 52...
A) A poker hand consists of five cards randomly dealt from a standard deck of 52 cards. The order of the cards does not matter. Determine the following probabilities for a 5-card poker hand. Write your answers in percent form, rounded to 4 decimal places. Determine the probability that exactly 3 of these cards are Aces. Answer: % Determine the probability that all five of these cards are Spades. Answer: % Determine the probability that exactly 3 of these cards...
A standard deck of 52 cards is shuffled and dealt. Let X1 be the number of...
A standard deck of 52 cards is shuffled and dealt. Let X1 be the number of cards appearing before the first ace, X2 the number of cards between the first and second ace (not counting either ace), X3 the number between the second and third ace, X4 the number between the third and forth ace, and X5 the number after the last ace. It can be shown that each of these random variables Xi had the same distribution, i=1,2,...,5, and...
Assume that 5 cards are dealt at random from a standard deck of 52 cards (there...
Assume that 5 cards are dealt at random from a standard deck of 52 cards (there are 4 suits in the deck and 13 different values (ranks) per each suit). We refer to these 5 cards as a hand in the rest of this problem. Calculate the probability of each of the following events when dealing a 5-card hand at random. (a) Exactly one pair: This occurs when the cards have numeric values a, a, b, c, d, where a,...
You are dealt one card from a deck of 52 cards. What is the probability of...
You are dealt one card from a deck of 52 cards. What is the probability of drawing the jack of clubs or the three of diamonds?
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT