A poker player holds a flush when all 5 cards in the hand belong to the same sui
ID: 3297715 • Letter: A
Question
A poker player holds a flush when all 5 cards in the hand belong to the same suit (clubs, diamonds, hearts, or spades). Recall that a standard deck of cards contains 52 cards, 13 of each suit, and that when the deck is well shuffled, each card dealt is equally likely to be any of those that remain in the deck. (a) What is the probability that the first card dealt is a spade? (b) What is the probability that the second card dealt is a spade, given that the first is a spade? (c) What is the probability that the third card dealt is a spade, given that the first two are spades? (d) What is the probability that the fourth card dealt is a spade, given that the first three are spades? (e) What is the probability that the fifth (and final) card dealt is a spade, given that the first four are spades? (f) Using your answers to (a) - (e), find the probability that you are dealt 5 spades. (g) The probability of being dealt 5 hearts or 5 diamonds or 5 clubs is the same as the probability of being dealt 5 spades. What is the probability of being dealt a flush?
Explanation / Answer
We know that a standard deck of cards contains 52 cards, 13 of each suit (clubs, diamonds, hearts, or spades).
a) The probability that the first card dealt is a spade = 13 / 52
= 0.25
b) The probability that the second card dealt is a spade, given that the first is a spade
= 12/51
c) The probability that the third card dealt is a spade, given that the first two are spades
= 11 / 50
d) The probability that the fourth card dealt is a spade, given that the first three are spades
= 10/49
e) The probability that the fifth (and final) card dealt is a spade, given that the first four are spades
= 9/48
f) The probability that you are dealt 5 spades
= 13/52 x 12/51 x 11/50 x 10 /49 x 9 /48
= 0.0004951981
g) As , the probability of being dealt 5 hearts or 5 diamonds or 5 clubs is the same as the probability of being dealt 5 spades.
Probability of dealing a flush
= 4 x (the probability of being dealt 5 cards of same suit)
= 4 x 0.0004951981
= 0.0019807923 or 0.198 %
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.