Question

Consider selecting two cards from a well-shuffled deck (unordered and without replacement). Let K1 denote the event the first card is a King and K2 the event the second card is a King. Let K1^K2 denote the intersection of the two events. a. Calculate P[K1^K2] as given by P[K1] P[K2 | K1]. b. Calculate the same probability using hands of size 2, and getting the quotient (# favorable hands)/(total # of hands).

Answer #1

Two cards are drawn without replacement from a well shuffled
deck of cards. Let H1 be the event that a heart is drawn first and
H2 be the event that a heart is drawn second. The same tree diagram
will be useful for the following four questions. (Note that there
are 52 cards in a deck, 13 of which are hearts)
(a) Construct and label a tree diagram that depicts this
experiment.
(b) What is the probability that the first...

From a well shuffled deck of 52 cards, are the events
"selecting an ace" and "selecting a hearts" dependent or
independents events? Please explain.

draw 20 cards without replacement from a shuffled, standard deck
of 52 cards. What is P (8th card is heart and 15th is spade)

You are dealt two cards successively without
replacement from a standard deck of 52 playing cards.
Find the probability that the first card is a king and the
second card is a queen.
I want the probability that both events will
occur. I do not want the probability of each
event.

Consider the following
experiment. Four cards are drawn out of a deck with
replacement from a well-shuffled deck of cards. The card
that is drawn out is either a heart or it is not a
heart. After a card is drawn out and recorded it is put
back into the deck and the deck is
reshuffled. Construct the binomial probability
function for x = 0, 1, 2, 3, 4
P(0) =
P(1) =
P(2) =
P(3) =
P(4) =

Two cards are drawn successively from an ordinary deck of 52
well-shuffled cards. Find the probability that a. the first card is
not
a Four of Clubs or an Five;
b. the first card is an King but the second is not;
c. at least one card is a Spade;

Two cards are successively dealt from a deck of 52 cards. Let A
be the event “the first card is a king” and B be event “the second
card is a ace.” Are these two events independent?

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...

11.3.47 Q13 Let two cards be dealt successively, without
replacement, from a standard 52-card deck. Find the probability of
the event. The first card is a ten and the second is a jack. The
probability that the first card is a ten and the second is a jack
is

You have a shuffled deck of n=15 cards: 0,…,14. You
deal out the 15 cards. Let Eidenote the event
that the ith card dealt was even, and let
Oi denote the event that the ith card
dealt was odd.
(a) What is P[E2|E1], the probability
that the second card is even given that the first card is even?
(b) What is P[E2|O1], the probability
that the second card is even given that the first card is odd?
(c) What is...

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