Question 4) The “flop” of a texas hold’em game consists of drawing at random two

ID: 3203323 • Letter: Q

Question

Question 4) The “flop” of a texas hold’em game consists of drawing at random two cards of a standard deck of 52, (ordering irrelevant).

a) How many distinct hands can you have in the “flop” of a texas hold’em game?

b) What is the chance of you drawing the ace and the king of spades?

c) What is the chance you will draw an ace and a king of the same suit?

d) What is the chance that you will draw two cards of spades?

e) What is the chance that you will draw two cards of the same suit?

f) What are the chances that you will draw either an ace and a king of the same suit or two cards of spades?

g) What is the chance that you will draw a pair (two equal cards of different suits)?

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I am struggling with this Econ Stat homework. Please help! Thank you :)

a) How many distinct hands can you have in the “flop” of a texas hold’em game?

ans: 52C2= 1326

b) What is the chance of you drawing the ace and the king of spades?

Ans: 4*1/52C2 = 0.00302

Since there are 4 aces in different suits

c) What is the chance you will draw an ace and a king of the same suit?

ans: =2*(chance of ace of spade)*(chance of king of spade) {since sequence doesn't matter}

= 2*(1/52)*(1/51)= 0.000754

d) What is the chance that you will draw two cards of spades?

ans: 13C2/52C2 = 0.0588

Since there are 13 cards of spades

e) What is the chance that you will draw two cards of the same suit?

ans: 4*(13C2/52C2) = 0.2353

since there are 4 different suits

f) What are the chances that you will draw either an ace and a king of the same suit or two cards of spades?

ans: add the 2 above (answered in c& d) probabilities

= 0.000754+.0588 =0.05956

g) What is the chance that you will draw a pair (two equal cards of different suits)?

ans: 13*4C2/52C2 = 0.058824

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