SOLUTION: concern 2-card hands from a standard 52-card deck.. A standard deck has13 cards from each of 4 suits (clubs, diamonds, hearts, spades). The 13 cards have face value 2 through10,

Question 369802: concern 2-card hands from a standard 52-card deck.. A standard deck has13 cards from each of 4 suits (clubs, diamonds, hearts, spades). The 13 cards have face value 2 through10, jack, queen, king, or ace. Each face value is a "kind" of card. The jack, queen, and king are "face cards."
20. What is the probability that exactly one card is a spade?
21. What is the probability that at least one card is a spade?
22. What is the probability that both cards are face cards?
23. What is the probability that both cards are spade face cards?
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a student takes a True/False quiz with 4 questions, each equally likely to be either T or F.
50. What is the probability of getting the first two questions correct?
52. What is the probability of getting all four questions correct given that the answers to the first two questions are correct?
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64. A directory on a computer's hard disk contains 12 files, 3 of which have viruses. If a file with a virus is selected, the virus is detected and another file is then selected. Find the expected number of files that must be selected before a virus-free file is found
Answer by jrfrunner(365) (Show Source): You can put this solution on YOUR website!
20. What is the probability that exactly one card is a spade?
P(Spade followed by NonSpade + Nonspade followed by Spade)=
(13/52)*(39/51)+(39/52)*(13/51)
21. What is the probability that at least one card is a spade?
=1-P(both NonSpade) = 1-39/52*(38/51)
22. What is the probability that both cards are face cards?
P(face followed by face)=16/52*(15/51)
23. What is the probability that both cards are spade face cards?
=4/52*(3/51)
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50. What is the probability of getting the first two questions correct?
P(CC)=1/2*1/2=1/4
52. What is the probability of getting all four questions correct given that the answers to the first two questions are correct?
P(four correct/first two correct)=P(last two correct)=1/2*(1/2)=1/4

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