Question

For each of the following situations indicate the appropriate distribution to model the random variable, X. 7.

Five cards are selected randomly, without replacement from a deck of 52 cards. Let X= the number of kings selected. Which model is appropriate? A. Hypergeometric B. Geometric C. Binomial D. None of these

8. Cards are selected randomly, without replacement from a deck of 52 cards until the first king is selected. Let X= the number of cards picked to get the first king. Which model is appropriate? A. Hypergeometric B. Geometric C. Binomial D. None of these

9. Five cards are selected randomly, with replacement from a deck of 52 cards. Let X= the number of kings selected. Which model is appropriate? A. Hypergeometric B. Geometric C. Binomial D. None of these

Answer #1

7. Hypergeometric distribution will be appropiate as becuse cards are selected without replacement and there are only 4 kings and 48 other cards. So, the random variable X keeps track how many kings are being drawn.

8. None of these. As both geometric and binomial distribution works with the assumption of with replacement and there is no question of hypergeometric.

9. Binomial distrinution with prametre n = 5 and p = 4/52 =1/13. As cards are drawn are with replacement and for finite number of times.

Suppose you are about to draw two cards at a random from a deck
of playing cards. Note that
there are 52 cards in a deck. Find the following
probabilities.
a. What is the probability of getting a Jack and then a King
(with replacement)?
b. What is the probability of getting a Heart or Jack and then a
2 (with replacement)?
c. What is the probability of getting an Ace and then a Queen
(without replacement)?
d. What is...

4. 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) a pair of any kind,
b) a pair of Kings, and
c) all four Kings.
5. Use the binomial theorem to expand (x + 3y)4 . You must
illustrate use of the binomial theorem

For which of the following counts would a binomial probability
model be reasonable?
All of the answer options are correct.
the number of sevens in a randomly selected set of five
digits
from your table of random digits, the number of hearts in a hand
of five cards dealt from a standard deck of 52 cards that has been
thoroughly shuffled
the number of phone calls received in a one-hour period

Five cards are selected at random without replacement from a
standard
deck of 52 cards. The order of the selection is not
considered.
Let S be the sample space connected to this experiment.
Let R be the event that all of the cards selected are red.
Let W be the event that none of the cards selected are hearts
a) Find n(S)
b) Find P(R)
c) Find P(W)
d) Find P(R|W)
e) Are the events R and W independent? Justify...

Determine whether or not the random variable X is a binomial random
variable. If so, give the values of n and p. If not, explain why
not.
a. X is the number of dots on the top face of fair die that is
rolled.
b. X is the number of hearts in a five-card hand drawn
(without replacement) from a well shuffled ordinary deck.
c. X is the number of defective parts in a sample of ten
randomly selected parts...

A standard deck consists of 52 cards of which 4 are aces, 4 are
kings, and 12 (including the four kings) are "face cards" (Jacks,
Queens, and Kings). Cards are dealt at random without replacement
from a standard deck till all the cards have been dealt. Find the
expectation of the following. Each can be done with almost no
calculation if you use symmetry.
a) The number of aces among the first 5 cards
b) The number of face cards...

Which of the following probabilities CANNOT be found using the
binomial distribution? a) The probability that 3 out of 8 tosses of
a coin will result in heads b) The probability of getting exactly
five face cards when drawing five cards without replacement from a
standard deck of 52 cards c) When randomly choosing a family with
four children, the probability that it will have exactly two boys
and two girls as children d) The probability that a student
randomly...

A special deck of 45 cards has 15 cards with a picture of a
ghost, 15 cards with a picture of a goblin, and 15 cards with a
picture of a witch.
a. 8 cards are picked in a row without replacement from this
special deck. Let X be the number of cards which are picked and
have a picture of a ghost. Find E(X) and V ar(X).
b. Repeat part a, but suppose 20 cards are picked instead of...

A standard deck of cards contains 4 suits (Hearts, Diamonds,
Spades, and Clubs) each containing 13 ranks (Ace, 2, 3, 4, 5, 6, 7,
8, 9, 10, Jack, Queen, King) for a total of 52 cards.
In a typical game of poker, you are dealt five cards (without
replacement) from a deck of 52 cards. How many Full Houses are
possible?
(A full house is a hand consisting of three of one rank and two
of another. For instance, three...

You randomly shuffle a 52-card deck of cards. We will consider
what happens as we draw 3 cards from the deck to form a sequence of
cards (for a - c) or a set of cards (d).
Answer each of the following questions, showing all relevant
calculations. You should analyze these using tree diagrams, but no
need to show the diagrams in your answer.
(a) Suppose you draw three cards from the deck with replacement;
what is the probability that...

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