PLEASE HELP SOLVE THIS PROBLEM AND SHOW ALL WORKINGS Determine the poker odds of drawing the following hand from a standard card deck. (4 suits, 13...

PLEASE HELP SOLVE THIS PROBLEM AND SHOW ALL WORKINGS

Determine the poker odds of drawing the following hand from a standard card deck. (4 suits, 13 ranks in each suit.)

What are the odds of drawing a full house (3 cards of one rank and 2 cards of another rank, or XXXZZ where XXX is 3 of a kind and ZZ is a pair)? Drawing cards is without replacement. (NOTE: If necessary, lay out 52 cards on a table and do dry run before computing the probabilities!)

In order to get a full house, you must pick the following 5 cards:

a.)      What is the probability that you will pick an X for your first card?

b.)     What is the probability that you will pick a second X your second card?

c.)      What is the probability that you will pick a third X for your third card?

d.)     What is the probability that you will pick a Z for your fourth card?

e.)    What is the probability that you will pick a second Z for your fifth card?

f.)     Now we picked the cards in the order X X X Z Z

We could have also picked the cards in many other orders such as

X X Z X Z,   X Z X X Z, etc.

Therefore you have to multiply your answer by a factor F to get the correct probability. This factor is

F =  , where 5 is for the 5 cards, 3 is for the 3 of a kind, and 2 is for the pair.

g.)     Multiply the above numbers (a) to (f) to get the final probability. Express you answer as 1/p (i.e., 0.10 = 1/10, 0.5 = 1/2).

(Note: The probability of getting a full house is 1/p = 1/694.17. If you did not get close to this number, then you did something wrong.)