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Probability

Section: Mathematics

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Question : 26 of 92

Marks: +1, -0

Two cards are drawn at random from a pack of 52 playing cards. If both the cards drawn are found to be black in colour, then the probability that atleast one of them is a face card is

[AP EAPCET 21 May 2025 S1]

$\;\frac{3}{13}$
$\;\frac{3}{5}$
$\;\frac{9}{65}$
$\;\frac{27}{65}$

Solution:

A=

Both cards are black

B=

At least one card is a face card.

P(A)=\;\frac{26}{52} \times \;\frac{25}{51}=\;\frac{650}{2652}

\because 20

Black card are not a face card.

\because P

(two black non-face card)

=\;\frac{20}{52} \times \;\frac{19}{51}=\;\frac{380}{2652}

P(B)=P(

two black card

)

-P

(two non-face card)

=\;\frac{650}{2652}-\;\frac{380}{2652}=\;\frac{270}{2652}

\because P\left(\frac{B}{A}\right) =\frac{\;\frac{270}{2652}}{\frac{650}{2652}}=\;\frac{270}{650}=\;\frac{27}{65}

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