Find the total number of possible 13card hands from an ordin

Find the total number of possible 13-card hands from an ordinary deck of 52 cards. If the hand is dealt at random, what is the probability that the hand contains the Ace of Dimond? What is the probability that the hand contains the Ace of Dimond and Ace of Club? What is the probability that the hand contains the Ace of Dimond or Ace of Club.

Solution

A)

There are 52C13 = 6.35014*10^11 13 card hands.

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B)

If the hand is dealt at random, what is the probability that the hand contains the Ace of Dimond?

If once card is already an Ace of Diamonds, then we can only choose 12 out of the remaining 51 in 51C12 = 1.58753*10^11 ways.

Thus,

P(A of D) = 1.58753*10^11/6.35014*10^11 13 = 0.25 [answer]

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c)

What is the probability that the hand contains the Ace of Dimond and Ace of Club?

We already fix 2 cards, so there are only 50C11 = 37353738800 ways to choose the other 11.

Hence,

P(A of D and A of C) = 37353738800/6.35014*10^11 = 0.058823529 [answer]

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d)

Note that

P(A of D OR A of C) = P(A of D) + P(A of C) - P(A of D and A of C) = 0.25 + 0.25 - 0.058823529

= 0.441176471 [ANSWER]