Question

# Seven cards are dealt from a deck of 52 cards. ​(a) What is the probability that...

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?

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