SOLUTION: Consider a standard deck of 52 cards (i) If you draw two cards from the deck without returning them. What is the probability that at least one will be a King? (ii) Four Queens a

Question 1082068: Consider a standard deck of 52 cards
(i) If you draw two cards from the deck without returning them. What is the probability that at
least one will be a King?
(ii) Four Queens are removed from the deck and placed face down on the table. If you turn over two of these cards, what is the probability that one is a red Queen and the other is a black Queen?

Answer by math_helper(2461) (Show Source): You can put this solution on YOUR website!
(i) P(Drawing two cards and having at least one be a king) is the same as 1 - P(no king appears in the draw)
and the latter is easier to calculate directly:
P (no king in a draw of 2 cards) = (48/52)*(47/51) = 564/663
P(rawing two cards and having at least one be a king) =
1 - 564/663 = 99/663 = or about 0.14932
=============
(ii) Say you pick the two cards one at a time from the 4 queens: P(red then black) + P(black then red) =
(2/4)*(2/3) + (2/4)*(2/3) = 8/12 =
�
This can be also be seen by the number of arrangements possible for the 4 queens:
RRBB, RBRB, RBBR, BBRR, BRBR, BRRB and say you just deal out the first two of these, exactly
4 out of the 6 possible arrangements will give you one R and one B.

RELATED QUESTIONS
If you draw 5 cards from a standard 52 card deck, what is the probability of getting 5... (answered by stanbon)

You draw two cards from a standard deck of cards (52 total cards), without replacing the... (answered by Fombitz,dkppathak)

If you draw two cards from a standard deck of 52 cards without replacement. Find P(2... (answered by Edwin McCravy)

Consider a standard deck of playing cards (52 cards, no jokers). If you draw two cards,... (answered by Edwin McCravy)

What is the probability of drawing all red cards from a standard deck of 52 cards if you... (answered by stanbon)

Two cards are drawn in succession, without replacement, from a standard deck of 52 cards. (answered by scott8148)

Assume I shuffle together two standard (52 card) decks of playing cards: If I draw a... (answered by greenestamps,ikleyn)

Two cards are drawn without replacement from a standard deck of 52 playing cards. What (answered by Theo)

You draw a two-card hand from a standard deck of 52 cards. What is the probability of... (answered by math_helper)