Question 2. Draw three cards without
replacement from a deck of cards and let X be the number of spades
drawn. Sketch the pmf of X and compute E(X).
Question 3. A fair coin is flipped n times.
What is the probability of getting a total of k heads if
a) The first flip shows heads
b) The first flip shows tails
c) At least one flip shows heads
We draw 6 cards from a 52 card deck and let X = the number of
heart cards drawn.
a. What is the expected value of X?
b. What is the variance of X? What is the standard deviation of
X?
Suppose three cards are drawn without replacement from a
standard deck of cards. A standard deck of cards contains 52 cards,
each card is one of 4 types (hearts, diamonds, spades, clubs) and
cards within each type are labelled 2, 3, 4, …, 10, J, Q, K, A.
Compute the probability for each of the following.
a. All three cards selected is a Heart.
b. All three cards selected is a King.
c. None of the three cards is either...
You draw two cards from a standard deck of 52 cards, but before
you draw the second card, you put the first one back and reshuffle
the deck. (Round your answer to three decimal places)
1) Find P(Ace on first card and Red card on second card)
2) Find P(Ace and King in either order)
3) If you do not replace the first card before drawing the
second card, Find P(Ace on first card and King on second card)
A standard deck of 52 cards is shuffled and dealt. Let X1 be the
number of cards appearing before the first ace, X2 the number of
cards between the first and second ace (not counting either ace),
X3 the number between the second and third ace, X4 the number
between the third and forth ace, and X5 the number after the last
ace. It can be shown that each of these random variables Xi had the
same distribution, i=1,2,...,5, and...
You draw cards from a standard deck of 52 playing cards. There
are 12 “face cards” in the deck (J, Q, or K). Let X be the number
of drawings (with replacement) it takes until you get your first
face card. Let Y be the number of drawings (with replacement) it
takes until you get your fifth face card. Let Z be the number of
face cards removed if you draw 10 cards without replacement.
(a) Calculate P(X = 5)....
Two cards are drawn at random from a standard deck of 52 cards.
The number of aces drawn is counted. Prepare a probability
distribution for this random experiment. Hint: Find the
probability that no aces are drawn, exactly one ace is drawn,
etc.
4. The experiment is to draw a card from a standard deck of
cards. Consider the following events: Q = drawing a Queen R =
drawing a red card
a. Are Q and R mutually exclusive? Clearly explain.
b. Find P(Q) and P(Q|R).
c. Are the events Q and R independent? Clearly explain.
draw 20 cards without replacement from a shuffled, standard deck
of 52 cards. What is the conditional probability P (12th card and
20th card is a heart 3rd card is a club)
Three cards are randomly selected from a deck of 52 cards. After
every draw, the card is NOT replaced back in the deck. Find the
probability of drawing a King, followed by two Aces in a row.
An instructor gives a pop quiz consisting of 10 multiple choice
questions, where each question has 5 choices, (a) through (e). What
is the probability of passing the pop quiz if you guess the answers
and you have to get 8 questions correct?...