Question

1. If two cards are drawn at random in succession from a standard 52-card deck without replacement and the second card is a club card, what is the probability that the first card is king card?

2. Let A and B be two events in a sample S. Under what condition(s) is P(A l B) equal to P(B l A) ?

3. If two events A and B are mutually Exclusive. Can A and B be Independent? Why or why not

Answer #1

Two cards are chosen at random from a standard 52-card deck.
Consider the events: A = first card is the ace of spades B = second
card is the ace of spades. Suppose the two cards are selected with
replacement.
i. Are the events A and B independent? Why?
ii. Are the events A and B mutually exclusive? Why?
Now suppose the two cards are selected without replacement.
iii. Are the events A and B mutually exclusive? Why?
iv. Are...

Suppose two cards are drawn in succession (without replacement)
from a standard deck of cards.
What is the probability that a face card is drawn first? (Enter
your probability as a fraction.)
What is the probability that a face card is drawn second, given
that a face card was drawn first? (Enter your probability as a
fraction.)
What is the probability of drawing two cards in succession
(without replacement) from a standard deck and having them both be
face cards?...

A card is drawn at random from a standard deck of cards . Let A
be the event "card is a spade" and let B be the event "card is a
king". a) Are A & B mutually exclusive ? b)Are A & B
independent ?

Consider a standard 52-card deck from which one card is
randomly selected and not replaced. Then, a second card is randomly
selected. Define the two events as given. Complete parts a) and b)
below.
A = The first card is a club
B = The second card is a king
Are these two events mutually exclusive? Why or why not?
A.The events are not mutually exclusive. The event of selecting
a club card as the first card cannot occur at...

Two cards are drawn without replacement from a standard deck of
52 playing cards. What is the probability of choosing a face card
for the second card drawn, if the first card, drawn without
replacement, was a jack? Express your answer as a fraction or a
decimal number rounded to four decimal places.

A card is randomly selected from a standard, 52-card deck. The
denomination on the card is recorded so that the resulting sample
space is {A, 2, 3, 4, 5, 6, 7, 8, 9, 10, K, Q, J}. (In other words,
we ignore the suits.) (a) (5 points) Given that the card selected
displays some number from 3 to 10 (inclusive), what is the
probability that the value on the card is not a multiple of 4? (b)
(5 points) Suppose...

Suppose that two cards are randomly selected from a standard?
52-card deck. (a) What is the probability that the first card is a
club and the second card is a club if the sampling is done without?
replacement? (b) What is the probability that the first card is a
club and the second card is a club if the sampling is done with?
replacement?

Three cards are drawn from a deck without replacement.
Find the probability the first card is a club, the second card
is a heart, and the third card is a black card.
Let A = 1st club Let B = 2nd heart Let C = 3rd black card
P( 1st club and 2nd heart and 3rd black card )
Write Answer as a Fraction (Not Simplified)
Write Answer as a Percent Round to Two Decimal Places =

Cards are drawn from a standard 52 card deck. After each card is
drawn, it is put back in the deck and the cards are reshuffled so
that each card drawn is independent of all others. Let N be the
random variable that represents the number of cards that are drawn
before the second appearance of an Ace. For example, if the
sequence of cards drawn was {2, 5, K, 7, A, 5, 3, J, A, ...} then N
would...

Two cards are selected at random from a standard 52-card deck
without replacement. Find the probability the first card is the 7
of Diamonds (♦) and the second card is a Club (♣).
Give your answer as a decimal rounded to 4 decimal places

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