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Probability

Section: Mathematics

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Question : 4 of 92

Marks: +1, -0

Two cards are drawn from a pack of 52 playing cards one after the other without replacement. If the first card drawn is a queen, then the probability of getting a face card from a black suit in the second draw is

[AP EAPCET 24 May 2025 S1]

$\;\;\frac{11}{663}$
$\;\;\frac{11}{1326}$
$\;\;\frac{11}{312}$
$\;\;\frac{11}{156}$

Solution:

Probability of drawing a black queen first

=\;\frac{2}{52}

Remaining black face card

=5

Probability of drawing a black face card after a black queen

=\;\frac{5}{51}

Now, probability of red queen first

=\;\frac{2}{52}

Probability of a black face card after a red queen

=\;\frac{6}{51}

So, total probability

=\;\frac{2}{52} \times \;\frac{5}{51}+\;\frac{2}{52} \times \;\frac{6}{51}

=\;\frac{10}{2652}+\;\frac{12}{2652}=\;\frac{22}{2652}=\;\frac{11}{1326}

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