A deck of 11 cards contains 4 red and 7 green cards. Shuffle
this deck, then deal 5 cards to Alice and 6 cards to Bob (without
any replacement, of course). Let X be the number of red cards that
Alice gets, and Y the number of red cards that Bob gets. (a) Write
down the joint probability mass function of X and Y . (Write a
formula rather than a table.) (b) Are X and Y independent? (c)
Compute...
10. How many ways are there to choose 5 cards from 52 deck of
cards to obtain (a) a full house? That is, of the from aaabb with a
and b distinct denominations. (b) a three of a kind? That is, of
the form aaabc where a, b, c are have distinct denominations?
Ans: (a) 3,744; (b) 54,912
Suppose you have a deck of 40 cards, containing 10 red cards and
30 black cards. A player draws 7 cards from the deck and places
them into their hand. The remaining deck of 33 cards has 5 red
cards and 5 black cards in the top 10 cards. The other 23 cards in
the remaining deck are unknown color. What is the probability of
the player's hand having 0,1,2,3,4,5 red cards?
A special deck of cards has 5 red cards, and 4 purple cards. The
red cards are numbered 1, 2, 3, 4, and 5. The purple cards are
numbered 1, 2, 3, and 4. The cards are well shuffled and you
randomly draw one card. R = card drawn is red E = card drawn is
even-numbered a. How many elements are there in the sample space?
b. P(E) = Round to 4 decimal places.
Pick two cards at random from a well-shuffled deck of 52
cards (pick them simultaneously so they are not the same card).
There are 12 cards considered face cards. There are 4 cards with
the value 10. Let X be the number of face cards in your hand. Let Y
be the number of 10's in your hand. Explain why X and Y are
dependent.
6.12.
Use R to pick 5 cards from a deck of 52. Did you get a pair or
better? Repeat until you do. How long did it take?
6.9.
How much area is to the right of 1.5 for a normal (0,2)?
Solve using R software
You pick cards one at a time without replacement from an
ordinary deck of 52 playing cards. What is the minimum number of
cards you must pick in order to guarantee that you get a) three of
a kind, and b) three Kings. Use the binomial theorem to expand (2x
+ y)^6. You must illustrate use of the binomial theorem.
You pick two cards, with replacement, from a standard 52 card
deck. The probability that both are red 7's is approximately:
Question options:
.0001
.0027
.0015
.0004
A “Remski Deck” is a deck of cards consisting of nine cards in
each of 10 denominations, A, 2, 3, 4, 5, 6, 7, 8, 9 and 10. In each
denomination there are three cards in each of the three suits
Harps: (H), Scythes (S) and Roses (R). So there are three different
2H, three different 10S, etc. for a total of 90 cards. A “hand” of
eight cards is dealt. In a hand, the order the cards are dealt...