Question

Seven cards are dealt from a deck of 52 cards.

(a) What is the probability that the ace of spades is one of the 7 cards?

(b) Suppose one of the 7 cards is chosen at random and found not to be the ace of spades. What is the probability that none of the 7 cards is the ace of spades?

(c) Suppose the experiment in part (b) is repeated a total of 10 times (replacing the card looked at each time), and the ace of spades is not seen. What is the probability that the ace of spades actually is one of the 7 cards?

Answer #1

**Answer:**

a)

Given,

probability that the ace of spades is one of the 7 cards = 51C6 / 52C7

we know,

nCr = n!/(n-r)!*r!

51C6 = 51!/(6!(51−6)! = 18009460

52C7 = 52!/(7!(52−7)!) = 133784560

Probability = 18009460 / 133784560

= 0.1346

b)

probability that none of the 7 cards is the ace of spades = 1 - probability that the ace of spades is one of the 7 cards

= 1 - 0.1346

= 0.8654

c)

probability that the ace of spades actually is one of the 7 cards = (probability that none of the 7 cards is the ace of spades)^10

= 0.8654^10

= 0.2356

Two cards are dealt from a standard deck of 52 cards. Find the
probability of getting:
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(b) At least one red card?

1. Suppose that 5 cards are dealt from a standard deck of 52
cards. What is the probability that one of those cards is the Ace
of Spades?

Please Explain!
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b. What is the probability that at least one of the cards is an
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