Question

(52 cards) Five cards are dealt from a shuffled deck. What is the probability that the 5 cards contain: 1) exactly one ace 2) at least one ace

Answer #1

**Answer:-1)** The solution can be found as-

Number of ways of choosing one ace from 4 aces is =
^{4}C_{1} = 4

Number of ways of choosing 4 other cards from 48 (non ace cards) =
^{48}C_{4} = 194580

Now, total number of ways of choosing 5 cards from 52 cards =
^{52}C_{5} = 2598960

**Thus probability of exactly one ace = (4 x
194580)/(2598960) = 0.2995 or 29.95 %**

**Answer:-2)** The number of ways of choosing 5
cards with no ace = ^{48}C_{5} = 1712304

Total number of ways of choosing 5 cards from 52 =
^{52}C_{5} = 2598960

Thus probability of no ace = 1712304/2598960 = 0.6588

So probability of getting at least one ace = 1 - 0.6588 = 0.3412 or 34.12 %

If 5 cards are dealt from a shuffled deck of 52 cards, find the
probability that none of the 5 cards are picture cards.
A. 1/216580
B. 3/13
C. 108257/108290
D. 33/108290

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(c) Suppose the experiment in part (b) is repeated a total of
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Please Explain!
Two cards are dealt uniformly at random from an ordinary deck of
52 cards.
a. What is the probability that both cards are aces and one of
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b. What is the probability that at least one of the cards is an
ace?

Problem 31: Two cards are dealt from an ordinary deck of 52
cards. This means that two cards are sampled uniformly at random
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a What is the probability that both cards are aces and one of
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b What is the probability that at least one of the cards is an
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b) If the cards are not replaced after being chosen, why is it
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