Question

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) =

Answer #1

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.The probability of drawing heart =13/52

Let X be the number of hearts drawn.

Therefore X is independently and identically distributed as binomial distribution with n=4, p=13/52=0.25.

Therefore the binomial probability function for x = 0, 1, 2, 3, 4 is given by

P(0)=0.3164063

P(1)=0.421875

P(2)=0.2109375

P(3)=0.046875

P(4)=0.00390625

### By using R command:

> n=4

> p=(13/52)

> p

[1] 0.25

> dbinom(0,4,0.25)

[1] 0.3164063

> dbinom(1,4,0.25)

[1] 0.421875

> dbinom(2,4,0.25)

[1] 0.2109375

> dbinom(3,4,0.25)

[1] 0.046875

> dbinom(4,4,0.25)

[1] 0.00390625

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...

In an experiment, 20 cards are drawn with replacement from a
standard deck of 52 well shuffled cards. What is the probability
that at least 3 cards drawn are number cards (2 through 10)?

A card is drawn from a well-shuffled deck of 52 playing cards.
What is the probability that it is a queen or a heart?

Assume an ordinary deck of 52 cards that has been
well-shuffled.
1. What is the probability of drawing an eight and then drawing
another eight assuming the first card is put back in the deck
before the second draw?
2. What is the probability of drawing an eight and then drawing
another eight assuming the first card is NOT put back in the deck
before the second draw?
3. What is the probability of drawing at least one card that...

A card is drawn at random from a well-shuffled deck of 52
cards. What is the probability of drawing a face card or a 3?
a. 48/52
b. 2/13
c. 4/13
d. 16

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;

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

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).

The following exercise refers to choosing two cards from a
thoroughly shuffled deck. Assume that the deck is shuffled after a
card is returned to the deck. If you do not put the first card back
in the deck before you draw the next, what is the probability that
the first card is a spade and the second card is a heart? (Enter
your probability as a fraction.)

I choose a card at random from a well-shuffled deck of 52 cards.
There is a 1/4 probability that the card is chosen is a spade, a
1/4 probability that the card is a heart, a 1/4 probability that
the card is a diamond, and a 1/4 probability that the card is a
club. Both spades and clubs are black cards, whereas hearts and
diamonds are red. What are the events of the card is a heart and a
card...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 23 minutes ago

asked 57 minutes ago

asked 59 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 3 hours ago