Question

3) Two cards are drawn from deck, with replacement. (This means that one person chooses a card,looks at it and returns it, and then another person chooses a card, looks at it, and returns it.) What is the probability that ...

(a) ... the first card is an ace and the second card is black?

(b) ... both cards are spades?

(c) ... neither card has a value from {2, 3, 4, 5}?(d) ... at least one card is an ace?

(e) ... the first card is an ace or the second card is black?

(4) An urn contains 7 red marbles labeled {1,2,3,4,5,6,7} and 5 green marbles labeled {1,2,3,4,5}.Four marbles are pulled out at once (i.e. with no particular order). What is the probability that ...

(a) ... all four marbles are red?

(b) ... more of the marbles are green than red?

(c) ... both red and green marbles are present?

(d) ... two of the marbles chosen are both labeled "5"?

Answer #1

Three cards are drawn with replacement from a standard deck.
What is the probability that the first card will be a diamond, the
second card will be a black card, and the third card will be an
ace? Express your answer as a fraction or a decimal number rounded
to four decimal places.

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?...

Three cards are drawn with replacement from a standard deck.
What is the probability that the first card will be a heart, the
second card will be a red card, and the third card will be a queen?
Express your answer as a fraction or a decimal number rounded to
four decimal places.

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...

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.

Probabilities with a deck of cards. There are 52 cards in a
standard deck of cards. There are 4 suits (Clubs, Hearts, Diamonds,
and Spades) and there are 13 cards in each suit. Clubs/Spades are
black, Hearts/Diamonds are red. There are 12 face cards. Face cards
are those with a Jack (J), King (K), or Queen (Q) on them. For this
question, we will consider the Ace (A) card to be a number card
(i.e., number 1). Then for each...

Three cards are drawn with replacement from a standard deck of
5252 cards. Find the the probability that the first card will be a
diamond, the second card will be a red card, and the third card
will be a ten. Express your answer as a fraction in lowest terms or
a decimal rounded to the nearest millionth.

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...

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...

1. Two cards are drawn from a well-shuffled ordinary
deck of 52 cards. Find the probability that they are both aces if
the first card is (a) replaced, (b) not replaced.
2. Find the probability of a 4 turning up at least once in two
tosses of a fair die.
3. One bag contains 4 white balls and 2 black balls; another
contains 3 white balls and 5 black balls. If one ball is drawn from
each bag, find the...

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