6. (+) 4 cards are randomly dealt to each of 13 players. (a) Describe the sample

Question

6. (+) 4 cards are randomly dealt to each of 13 players. (a) Describe the sample space and write down its size. (b) What is the probability of A- feach player has one card from each suit? (c) What is the probability of {each player has all four cards of the same value? (d) * Compute PB(A) and PA(B). Are A and B independent? (e) What is the probabiility that players one, two, and three have been dealt only aces, kings, or queens. (f) (**) What is the probability that one player has one card from each suit but that nobody As usual, explain. else has cards from more than one suit?

Explanation / Answer

A)
There are 52! ways to deal out the cards. However, the order of cards within a hand doesn't matter
Hence required number of possible ways to deal 4 cards is 52!/4!13

B)
There are 13 cards of each suit for player 1, 12 cards of each suit for player 2, and so on.

13^412^411^4 = 13!^4

P(A) = 13!^4/(52!/4!13)

C)
There are 13 possible hands for player 1, 12 possible hands for player 2, and so on.

Possible numbers are 13!

P(B) = 13!/(52!/4!13)

D)
Note that in order for a player to have four of the same value, they must be different suits. Thus,
P(A|B)=1

and
P(B|A) = P(B)/P(A) = 1/(13!^3)

It is also clear that the events are not independent.

Related Questions

Navigate

• Browse (All)
• Browse 6
• Subjects

---

---

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