Question

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 take on a value of N=8. Find the probability that N is equal to 17. Show all work! Thanks

Answer #1

The probability p of drawing an Ace during any given draw is

.

This probability will remain the same for each draw as the card is being replaced and the deck is reshuffled after each draw.

Let X be a random variable which indicates the number of draws required to get s=2 aces (which is 2 successes). Let the probability of sucess (getting an ace) be p=1/13.

We know that X has a Negative Biniomial distribution with the following probability

We have to remember here that x is the number of cards drawn including the second ace. But the random variable N represents the number of cards that are drawn before the second appearance of an Ace. That means N=X-1

Replacing we get the distribution of N as

We want the probability that N=-17

a
card is drawn from a standard deck of 52 playing cards. find the
probability that the card is an ace or a heart

Here is a table showing all
52
cards in a standard deck.
Face cards
Color
Suit
Ace
Two
Three
Four
Five
Six
Seven
Eight
Nine
Ten
Jack
Queen
King
Red
Hearts
A
♥
2
♥
3
♥
4
♥
5
♥
6
♥
7
♥
8
♥
9
♥
10
♥
J
♥
Q
♥
K
♥
Red
Diamonds
A
♦
2
♦
3
♦
4
♦
5
♦
6
♦
7
♦
8
♦
9
♦
10
♦
J...

If one card is drawn from a standard deck of 52 playing cards,
what is the probability of drawing a number card (Ace, 2-10)?

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.

i
have a hand that consists of 7 cards drawn from a standard 52 card
deck. whats the probablity of having a hand with entirely cards
that are not face cards/ an ace, or a hand with all clubs

A
card is drawn from a 52 card deck; then a second card is drawn;
then a third card is drawn. Find the probability of getting two
queens and then an ace.
a) With replacement?
b) Without replacement ?

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?

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...

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...

The following question involves a standard deck of 52 playing
cards. In such a deck of cards there are four suits of 13 cards
each. The four suits are: hearts, diamonds, clubs, and spades. The
26 cards included in hearts and diamonds are red. The 26 cards
included in clubs and spades are black. The 13 cards in each suit
are: 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, and Ace. This
means there are four...

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