label all variables. Please do not print the raw data provided for the exercise:

Question

label all variables. Please do not print the raw data provided for the exercise: only print your calculations, charts, and answers! Question 1 DO NOT USE EXCEL OR STATA FOR THIS QUESTION (20 marks) Imagine that you live in a simple world where a deck of cards has only four numbers (1,2,3, and 4) and 3 suits (red, white, and blue). And the only Poker game is three-card- no-draw. The possible poker hands therefore include: Royal Flush (2,3,4 in any one suit), Straight Flush (1,2,3 in any one suit), 3 of a Kind, Straight (1,2,3 or 2,3,4 with at least two suits represented), a Pair, a Flush (3 cards in the same suit), and Nothing. (a) How many different three-card hands are possible? Be sure to show all calculations. (5 marks) As there four numbers and 3 suits, the total number of cards is 3*4=12 Total number of cards-121( 12-3).312#1 1 * 10/6-220 (b) What is the probability of getting each of the hands listed above (round to 4 decimal places)? Be sure to show all calculations. (15 marks) Royal Flush=1+3C1/220-0.0136 Straight Flush-1*3C1/220-0.0136

Explanation / Answer

(a)

There are 3 suits and 4 cards for each suit and thus we have a total of 12 cards. Out of these 12 cards we have to pick 3 cards for a single hand.

The possible number of 3 card hands would be given by,

N = C(12,3) = 220

b)

Royal Flush :

There are only 3 possible scenarios of getting 2,3,4 of a same suit. Hence the probability of getting a Royal Fluh would be given by,

P = C(3,1)/220 = 0.0136

Straight Flush :

In this case also there are only 3 scenarios possible. Hence the probability of getting a straight flush would be given by,

P = C(3,1)/220 = 0.0136

3 of a kind :

There are 4 scenarios(when 3 cards of same rank are selected. Hence the required probability would be given by,

P = 4/220 = 0.0182

Straight :

The required probability would be given by,

P = 2*(C(3,1)*C(3,1)*C(3,1)-3)/220 = 0.2364

A pair :

Here we will have two cards of one suit and third card of a different suit. Its probability would be given by,

P = C(4,1)*C(3,2)*C(9,1)/220 = 0.4909

Flush :

The required probability would be given by,

P = C(3,1)*C(4,3)/220 = 0.0545

Nothing :

P = 1 - 0.0136 - 0.0136 - 0.0182 - 0.2364 - 0.4909 - 0.0545 = 0.1728

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