In five-card poker, a ”flush” is a hand where all five cards are from the same s
ID: 3273410 • Letter: I
Question
In five-card poker, a ”flush” is a hand where all five cards are from the same suit. A ”straight” is a hand where all five cards are in sequential order, e.g. 9-8-7-6-5. Suppose you have the following cards: the 5 of clubs, 6 of clubs, 8 of hearts, 9 of clubs, 10 of diamonds.
a. If you replace the 8 of hearts and 10 of diamonds from your hand with two random cards from the cards left in the deck, what is the probability that both of the cards you draw will be clubs to create a flush?
b. If you replace the 5 of clubs from the deck with a random card left in the deck, what is the probability that the card you draw will be a 7 to create a straight?
c. You think that you will win the hand if you can create either a straight or a flush, and will lose if you cannot. Should you aim to create a straight, or a flush?
Explanation / Answer
a) as there are 10 remaining club cards out of remaining 47 cards.
therefore probability that both of the cards you draw will be clubs to create a flush =(10/47)*(9/46)=0.0416
b)as there are 4 card of 7 out of 47 cards.
probability that the card you draw will be a 7 to create a straight =4/47=0.0851
c)as probability of creating a straight is higher ; you should try for straight.