Q. 2.16 Poker dice are played by simulta... [FREE SOLUTION]

91影视

A First Course in Probability

Sheldon M. Ross

$Math Studyset 91影视 Explanations$ Math

9th Edition 路 432 pages

ISBN: 9780321794772

Chapter 2: Q. 2.16 (page 49)

Poker dice are played by simultaneously rolling $5$ dice. Show that
$(a) P (n o t w o a l i k e) = . 0926; (b) P (o n e p a i r) = . 4630; (c) P (t w o p a i r) = . 2315; (d) P (t h r e e a l i k e) = . 1543; (e) P (f u l l h o u s e) = . 0386; (f) P (f o u r a l i k e) = . 0193; (g) P (f i v e a l i k e) = . 0008 .$

Short Answer

Expert verified

$(a) P (n o t w o a l i k e) = 0.0926 (b) P (o n e p a i r) = 0.4630 (c) P (t w o p a i r s) = 0.2315 (d) P (t h r e e a l i k e) = 0.1543 (e) P (F u l l h o u s e) = 0.0386 (f) P (F o u r a l i k e) = 0.0193 (g) P (F i v e a l i k e) = 0.0008$

Step by step solution

Given Information.

Poker dice are played by simultaneously rolling $5$ dice.

Part (a) Explanation.

$P (no two alike) = \frac{6 脳 5!}{6^{5}} = 0.0926$ .

Part (b) Explanation.

$P (one pair) = \frac{(\begin{matrix} 5 \\ 2 \end{matrix}) (\begin{matrix} 6 \\ 1 \end{matrix}) (\begin{array}{l} 5 \\ 3 \end{array}) 3!}{6^{5}} = 0.4630$ .

Part (c) Explanation.

$P (two pairs) = \frac{(\begin{array}{l} 5 \\ 2 \end{array}) (\begin{array}{l} 3 \\ 2 \end{array}) (\begin{array}{l} 6 \\ 2 \end{array}) (\begin{array}{l} 4 \\ 1 \end{array})}{6^{5}} = 0.2315$ .

Part (d) Explanation.

$P (three alike) = \frac{(\begin{matrix} 5 \\ 3 \end{matrix}) (\begin{array}{l} 6 \\ 1 \end{array}) (\begin{array}{l} 5 \\ 2 \end{array}) 2!}{6^{5}} = 0.1543$ .

Part (e) Explanation.

$P (Fullhouse) = \frac{(\begin{array}{l} 5 \\ 3 \end{array}) (\begin{array}{l} 6 \\ 1 \end{array}) (\begin{array}{l} 5 \\ 1 \end{array})}{6^{5}} = 0.0386$ .

Part (f) Explanation.

$P (Four alike) = \frac{(\begin{array}{l} 5 \\ 4 \end{array}) (\begin{array}{l} 6 \\ 1 \end{array}) (\begin{array}{l} 5 \\ 1 \end{array})}{6^{5}} = 0.0193$ .

Part (g) Explanation.

$P (Five alike) = \frac{(\begin{array}{l} 6 \\ 1 \end{array})}{6^{5}} = 0.0008$ .

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Course	Choices
Entree	Chicken or roast beef
Starch	Pasta or rice or potatoes
Dessert	Ice cream or Jello or apple pie or a peach

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Short Answer

Step by step solution

Given Information.

Part (a) Explanation.

Part (b) Explanation.

Part (c) Explanation.

Part (d) Explanation.

Part (e) Explanation.

Part (f) Explanation.

Part (g) Explanation.

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91影视

Poker dice are played by simultaneously rolling 5dice. Show that(a)P(notwoalike)=.0926;(b)P(onepair)=.4630;(c)P(twopair)=.2315;(d)P(threealike)=.1543;(e)P(fullhouse)=.0386;(f)P(fouralike)=.0193;(g)P(fivealike)=.0008.

Short Answer

Step by step solution

Given Information.

Part (a) Explanation.

Part (b) Explanation.

Part (c) Explanation.

Part (d) Explanation.

Part (e) Explanation.

Part (f) Explanation.

Part (g) Explanation.

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

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