Answered: In a game of Texas Hold’em, what is the…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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In a game of Texas Hold’em, what is the probability that your hole cards will be face cards and the same suit? (Note: There is no specific formula for this. Think about the cards and use combinations.)

Expert Solution

Step 1 the probabilities

Following probabilities are needed to be calculated.

$\begin{array}{rcl} P (two face cards of spade) & = & \frac{{}^{3}C_{2}}{{}^{52}C_{2}} \\ = & \frac{3}{1326} \\ = & \frac{1}{442} \end{array}$

Similarly

$\begin{array}{rcl} P (two face cards of club) \end{array} \begin{array}{rcl} = \end{array} \begin{array}{rcl} \frac{1}{442} \end{array} \begin{array}{rcl} \end{array} \begin{array}{rcl} P (two face cards of heart) \end{array} \begin{array}{rcl} = \end{array} \begin{array}{rcl} \frac{1}{442} \end{array} \begin{array}{rcl} \end{array} \begin{array}{rcl} P (two face cards of diamond) \end{array} \begin{array}{rcl} = \end{array} \begin{array}{rcl} \frac{1}{442} \end{array}$

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