I was wondering if anyone could help me with this lab? \"The game Texas Hold\'em

Question

I was wondering if anyone could help me with this lab?

"The game Texas Hold'em is a variation of the standard poker game. The game begins when each player is dealt two cards face down, called "hole cards". Subsequent cards are dealt, but we will be investigating the probability associated with the hole cards.

A. Assume that you are about to be dealt your hole cards, and that you are the first player. How any possible combinations of cards could you be dealt? Note that this would represent the number of ways to select 2 cards from 52.

B. The best possible set of hole cards is two aces. In how many ways can 2 aces be dealt?

C. Generalize from part (B.) and determine the number of ways to be dealt a "pocket pair", which consists of two cards of the same denomination.

D. Using our answers in (A.) and (C.) determine the probability of being dealt a "pocket pair".

E. Imagine that you play Texas Hold'em four times. Determine the probability distribution for X, the number of times you are dealt a pocket pair for your hole cards.

F. Determine the mean and standard deviation of X. Is the distribution of X symmetric, skewed right, or skewed left?

G. A limousine service has three cars (sedans) which it hires out by the day. The number of requests for these sedans, per day, is a Poisson random variable, (X), with mean 1.5.

Complete the following Probability Distribution Table:

H. What is the probability that the firm is able to meet the demand for its cars?

I. What is the probability of at least one car requested on a randomly selected day?

J. Graph the probability distribution found in (G.) and describe its shape.

Explanation / Answer

A) possible combinations of cards that be dealt = 52C2 = 1326

B) ways in which 2 aces can be dealt = 4C2 = 6 (as there are 4 different ace cards and we have to select 2 out of them)

C) number of ways to be dealt a "pocket pair" = 13 * 6 = 78 (as there are 13 different cards and each card has 4 of its type with their internal combination of 6)

D) probability of being dealt a "pocket pair = 78 / 1326 = 0.05823

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