A pack of playing cards was found to contain only 51 cards. If the first 13 cards which are examined are all red, what is the probability that the missing card is black.

Solution

Let E₁ the event that the missing card is black and E₂ be the event that the missing card is red.
Let A be the event the first 13 cards which are examined are all red.
$therefore space space space space straight P left parenthesis straight E subscript 1 right parenthesis space equals space 1 half semicolon space space space space space straight P left parenthesis straight E subscript 2 right parenthesis space equals space 1 half$
P(A/E₁) = Probability of selecting 13 red cards, when the missing card is black
$equals fraction numerator space straight C presuperscript 26 subscript 13 over denominator straight C presuperscript 51 subscript 13 end fraction$
P(A/E₂) = Probability of selecting 13 red cards, when the missing card is red
$equals space fraction numerator straight C presuperscript 25 subscript 13 over denominator straight C presuperscript 51 subscript 13 end fraction$

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Probability

A pack of playing cards was found to contain only 51 cards. If the first 13 cards which are examined are all red, what is the probability that the missing card is black.

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