Question

5 cards are drawn from a standard deck without replacement. What is the probability that at least one of the cards drawn is a spade? Express your answer as a fraction or a decimal number rounded to four decimal places.

Answer #1

A "standard" deck of playing cards consists of 52 Cards in each of the 4 suits of Spades, Hearts, Diamonds, and Clubs. Each suit contains 13 cards: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King.

hence

the total number of cards

we want the probability that at least one of the cards drawn is a spade.

we can use the following formula

in a spade suit, there are 13 cards.

let S be the event that none of the cards is spade then

5 cards are drawn from a standard deck without replacement then the probability of no spade is given by

hence

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.

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.

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.

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 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.

Five cards are drawn without replacement from a standard deck of
52 cards consisting of four suits of thirteen cards each. Calculate
the probability that the five cards result in a flush (all five
cards are of the same suit).

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)?

Three cards are drawn from a deck without replacement.
Find the probability the first card is a club, the second card
is a heart, and the third card is a black card.
Let A = 1st club Let B = 2nd heart Let C = 3rd black card
P( 1st club and 2nd heart and 3rd black card )
Write Answer as a Fraction (Not Simplified)
Write Answer as a Percent Round to Two Decimal Places =

Two cards are selected at random from a standard 52-card deck
without replacement. Find the probability the first card is the 7
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Give your answer as a decimal rounded to 4 decimal places

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

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