Two cards are drawn without replacement from a shuffled deck of 52 cards. What is the probability that the second card is a king?
Solutions showing step-by-step is very much appreciated.
Thank you in advance .
Hello, flywithme!
I can solve this The Long Way, but why bother?Two cards are drawn without replacement from a shuffled deck of 52 cards.
What is the probability that the second card is a King?
$\displaystyle P(\text{2nd is King}) \;=\;\frac{4}{52} \:=\:\frac{1}{13}$
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Do we care what the first card is? . . . No!
Suppose they asked for the probability that the 17th card is a King.
Do we need to know if any of the first 16 cards are Kings? . . . No.
Spread the cards face down on the table.
. . Point to any card: "Is it a King?"
The probability will be: .$\displaystyle \frac{4}{52} \,=\,\frac{1}{13}$
Get it?
I always talk about this in class.
I usually ask what is the probability we select the ace of spades on the second, fifth... pick?
It's always 1/52.
BUT then I prove it....
P(King on second pick)=P(KING, KING)+P(not a KING, KING)
$\displaystyle = \left({4\over 52}\right)\left({3\over 51}\right) +\left({48\over 52}\right)\left({4\over 51}\right) $
$\displaystyle = \left({4\over 52}\right)\left[{3\over 51}+{48\over 51}\right] $
$\displaystyle = {4\over 52}= {1\over 13} $