Question

Back to the cards! In poker, a flush is when all five cards are the same suit. Find the probability of being dealt a flush (when being dealt five cards).
Start by just considering clubs. a) What is the probability that the first card dealt is a club?
b) What is the probability that the second card dealt is a club given that the first one was a club?
c) What is the probability that the third card dealt is a club given that the first two were clubs?
d) What is the probability that the fourth card dealt is a club given that the first three were clubs?
e) What is the probability that the fifth card dealt is a club given that the first four were clubs?
f) The probability of being dealt all five clubs is the product of the above probabilities. Why is this true and what is this probability?
g) You have now found the probability of being dealt a flush in clubs. This is the same as the probability of being dealt a flush in diamonds, hearts, or spades. Then, what is the proability of being dealt a flush?

Answer 1

a) 13 we know that the number of clubs in the deck/52 that the total number of cards in the deck =0 .25= 25%.
b) 12 the remaining number of clubs in the deck/51 the remaining number of cards in the deck = 0.235= 23.5%.
c) 11 same as above/50 the same as above = 0.22= 22%
d) 10/49 = 20.4%
e) 9/48 = 18.75%
f) The combinations that can be made with certain characteristics are limited to say: ace of clubs to 12 other clubs, two of clubs to 12 other clubs, three of clubs to 12 other clubs, etc. As the desired outcome is reached, the probable outcome percentages must be multiplied together to accommodate all combinations. the probability is .049%.
g) probability of dealt a flush is 13*12*11*10*9*4/52*51*50*49*48 = 617,760/311,875,200 = 0.00198079232, or 0.2% when round up. This is any of the 13 cards needed in a particular suit, times any of the remaining 12, times any of the remaining 11 after that, and so on multiplied by 4 since there are four suits in which this can occur. This is divided by the number of cards in the deck 52 times the remaining cards when that's drawn, and so on and so forth.