For each question (a–e) below, choose one of the answers (i–viii); explain your choice.

questions a deck of cards is shuffled. what is the chance that— (a) the top card is the king of spades and the bottom card is the queen of spades? (b) the top card is the king of spades and the bottom card is the king of spades? (c) the top card is the king of spades or the bottom card is the king of spades? (d) the top card is the king of spades or the bottom card is the queen of spades? (e) of the top and bottom cards, one is the king of spades and the other is the queen of spades?

answers
(i) 1/52 × 1/51
(ii) 1/52 + 1/51
(iii) 1/52 × 1/52
(iv) 1/52 + 1/52
(v) 1−(1/52 × 1/51)
(vi) 1−(1/52 × 1/52)
(vii) 2/52 × 1/51
(viii) none of the above

Step-by-step explanation:

given that a deck of cards is shuffled.

we know in a deck there are 52 cards, 13 cards of each variety spade, clubs hearts and dice.  Red are 26 and black are 26.  kings, will be 4.

(a) the top card is the king of spades and the bottom card is the queen of spades?

(iii) 1/52 × 1/52

Top has 1/52 and bottom has 1/52 and these are independent.

(b) the top card is the king of spades and the bottom card is the king of spades?

(viii) None of the above

Because it is impossible.

(c) the top card is the king of spades or the bottom card is the king of spades?

(iv) 1/52 + 1/52

This is the sum of probabilities because there is no common event for these two.

(d) the top card is the king of spades or the bottom card is the queen of spades?

(ii) 1/52 + 1/51 (once king of spades is there, then probability is 1/51 for bottom card)

(e) of the top and bottom cards, one is the king of spades and the other is the queen of spades?

(vii) 2/52 × 1/51

Because this is twice of probability d.

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step-by-step explanation:

3

step-by-step explanation: