Question 3)You draw 4 cards in a row, from a deck of 52. a) What is the chances

ID: 3203238 • Letter: Q

Question

Question 3)You draw 4 cards in a row, from a deck of 52.

a) What is the chances that you will get 4 aces (hearts, clubs, diamonds, spades), in that order?

b) What are the chances that the set of 4 cards you draw will contain the all the 4 aces? (In other words, you will draw the 4 aces in any order).

c) What are the chances that you all your cards will be of spades? Is it close to 25%? Try to explain why.

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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 :)

Number of ways of selecting 4 cards out of 52 is C(52,4) = 270725

(a)

There is only one way of selecting 4 aces in the given order so the chances that you will get 4 aces in order (hearts, clubs, diamonds, spades) is

(1/52)*(1/51)*(1/50)*(1/49) = 0.000000154

(b)

Numebr of ways fo selecting 4 aces out of 4 aces is C(4,4) = 1 so

1 / 270725 = 0.00000369

(c)

There are total 13 spades so number of ways of selecting 4 spades out 13 is C(13, 4) = 715

So required probability is

715 / 270725 = 0.0026 = 0.26%

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