Question

5. Suppose a deck of 52 cards is shuffled and the top two cards are dealt.

a) How many ordered pairs of cards could possibly result as outcomes?

Assuming each of these pairs has the same chance, calculate:

b) the chance that the first card is an ace;

c) the chance that the second card is an ace (explain your answer by a symmetry argument as well as by counting);

d) the chance that both cards are aces;

e) the chance of at least one ace among the two cards.

6. Repeat Exercise 5, supposing instead that after the first card is dealt, it is replaced, and shuffled into the deck before the second card is dealt.

I need Question 6

Answer 1

6. a) How many ordered pairs of cards could possibly result as outcomes?

52*52 = 2704

b) the chance that the first card is an ace;

(52*4)/(52*52) = 1/13

c) the chance that the second card is an ace (explain your answer by a symmetry argument as well as by counting);

(52*4)/(52*52) = 1/13

d) the chance that both cards are aces;

(4 x 4)/(52 x 52) = 1/169

e) the chance of at least one ace among the two cards.

P(at least one ace)= 1/13 + 1/13 - 1/169

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