Question 250530: Suppose that 5 cards are selected with replacement from a standard deck of 52 playing cards. The
deck contains 13 denominations (ace, two, three, … , ten, jack, queen, king) of each of four suits
(hearts, diamonds, spades, and clubs). The kings, queens, and jacks are known as face cards. A card
is selected and its suit and denomination recorded. The card is replaced in the deck. The deck is
shuffled, and the process repeated 4 more times.
a. What is the probability that all five cards are face cards?
b. What is the probability that at least one card is a face card?
c. What is the probability that exactly one card is a face card?
d. What is the probability that no hearts are selected?
e. What is the probability one or fewer hearts are selected?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Suppose that 5 cards are selected with replacement from a standard deck of 52 playing cards. The deck contains 13 denominations (ace, two, three, … , ten, jack, queen, king) of each of four suits (hearts, diamonds, spades, and clubs). The kings, queens, and jacks are known as face cards.
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A card is selected and its suit and denomination recorded. The card is replaced in the deck. The deck is shuffled, and the process repeated 4 more times.
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a. What is the probability that all five cards are face cards?
Since the cards are replaced the selections are independent.
P(a face card in one draw) = 12/52
P(5 face cards in 5 draws) = (12/52)^5
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b. What is the probability that at least one card is a face card?
P(at least one) = 1 - P(none)
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P(no face card in 5 draws) = (40/52)^5
P(at least one face card in 5 draws) = 1 - (40/52)^5
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c. What is the probability that exactly one card is a face card?
It's binomial with n= 5 ; p = 12/52, x = 1
binompdf(5,12/52,1) = 0.4040
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d. What is the probability that no hearts are selected?
(3/4)^5
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e. What is the probability one or fewer hearts are selected?
binomial with n=5, p= 3/4, 0<= x <=1
binomcdf(5,3/4,1) = 0.0156
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Cheers,
Stan H.
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