if 4 cards are randomly selected without replacement from a deck
of cards, what is the...
if 4 cards are randomly selected without replacement from a deck
of cards, what is the probability of getting at least one ace (
exact reduced fraction or decimal or round to 3 significant
digits)?
From shuffled deck of cards, 4 cards are randomly selected
without replacement from shuffled deck of 52 cards. What is the
probability to get at least one ace?
Two cards are randomly selected from a deck of 52 cards
without replacement. Define two events:
A = { The first
card is a King. }
B = { The second
card is a King. }
What is P (A)?
What is P (B)?
What is P (A ∩ B)?
What is P (A|B)?
What is P (A ∪ B)?
Are A and B independent? Give your
reason.
Define a random variable Y be the number of Kings.
Find the...
Three cards are drawn from a deck of 52 cards without
replacement.
(a) What is the probability that the third card is a spade (♠)
given that the first card is a spade?
(b) What is the probability that all cards are spades given that
at least one of them is a spade?
(c) Let Y be the number of black cards drawn. What is the
probability that all 3 cards are black given that the first card is
a...
Three cards are drawn from a deck of 52 cards without
replacement.
(a) What is the probability that the third card is a spade (♠)
given that the first card is a spade?
(b) What is the probability that all cards are spades given that
at least one of them is a spade?
(c) Let Y be the number of black cards drawn. What is the
probability that all 3 cards are black given that the first card is
a...
Three cards are randomly drawn, without replacement, from an
ordinary deck of 52 cards. Find each of the following.
a. The probability of drawing, in order, one 10, one spade and
one black jack.
b. The probability that in any order, one queen, one spade and
one black ace are drawn.
c. The probability of drawing exactly three kings.
d. The probability of drawing exactly one ace.
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...
Two cards are randomly selected from a deck of 52 playing cards.
(a) What is the probability they constitute a pair (that is, that
they are of the same denomination)? (b) What is the conditional
probability they constitute a pair given that they are of different
suits?
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)
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