Question

suppose you draw two cards (a sequence) from a standard 52-card deck without replacement.

Let A = "the first card is a spade" and B = "the second card is an Ace." These two events "feel" (at least to me) as if they should be independent, but we will see, surprisingly, that they are not. A tree diagram will help with the analysis.

(a) Calculate ?(?)

(b) Calculate ?(?)

(c) Calculate ?(?|?)

(d) Show that A and B are not independent (trivial, just observe that the results of (a) and (c) are different!).

Answer #1

We draw cards, one by one, without replacement, from a deck of
52 cards. Calculate the probability that the first ace will appear
in the k-th draw, if we know that the n-th card was a spade, and
the m-th card was not a club. k=42,m=18,n=4

Consider a standard 52-card deck. If you draw 25% cards from the
deck without replacement.
What is the probability that your hand will contain one ace?
What is the probability that your hand will contain no ace?

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...

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 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...

Suppose 2 cards are drawn randomly for a standard 52 card
deck.
What is the probability that the second card is a face card (J,
Q, or K) when the two cards are drawn without replacement?
I'm stuck on this question, my hint was to draw a tree diagram
to calculate the probability.

1. Suppose you draw two cards from a deck of 52 cards without
replacement.
a. What’s the probability that the ﬁrst draw is a heart and the
second draw is not a heart?
b. What’s the probability that exactly one of the cards are
hearts?
c. If you draw two cards with replacement, what’s the
probability that none of the cards are hearts?

We are drawing two cards without replacement from a standard
52-card deck. Find the probability that we draw at least one
red card.
The probability is
nothing.

Draw three cards from a standard 52 cards deck without
replacement. What is the probability of having an Ace in those
three cards- given you got all three different rank
cards.

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...

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