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)
Total number of cards = 3*4 = 12

Possible number of 3-Card hands = 12C1 * 11C1 * 10C1 = 12 * 11 * 10 = 1320

(b)
Royal Flush: Only 3 possible ways of getting royal flush
Hence P(Royal Flush) = 3/1320 = 0.00227

Straight Flush: Only 3 possible ways of getting a straight flush
Hence P(Straight Flush) = 3/1320 = 0.00227

3 of a Kind: Any number in all suits, there are 4 possible ways for this
Hence P(3 of a Kind) = 4/1320 = 0.00303

Straight : Cosidering no restriction of suit, possible number of straights are 4C1*4C1*4C1 for combination (1,2,3) and 4C1*4C1*4C1 for combination (2,3,4). Total straights are 4^3*2 = 128
Remove Royal and straight flush 128 - 6 = 122

P(Straight) = 122/1320 = 0.0924

A pair: Any number can form a pair which can be selected in 4C1 ways and third card can be selected from remaining 9 cards in 9 ways. Possible ways are 4*9 = 36

P(A pair) = 36/1320 = 0.02727

A Flush: Possible ways are 4C3*3 = 12
P(A Flush) = 12/1320 = 0.00909

Nothing: 1320 - (3 + 3 + 4 + 122 + 36 + 12) = 1140
P(Nothing) = 1140/1320 = 0.8636

Related Questions

Navigate

• Browse (All)
• Browse L
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.