A card is picked at random from a pack of 52 ...

CBSE Class 12 Math 2020 Delhi Set 1 Solved Paper

Question : 9 of 36

Marks: +1, -0

A card is picked at random from a pack of 52 playing cards. Given that the picked card is a queen, the probability of this card to be a card of spade is

$\;\frac{1}{3}$
$\;\frac{4}{13}$
$\;\frac{1}{4}$
$\;\frac{1}{2}$

Solution: 👈: Video Solution

Let event

A=

Picked card is a queen. and event

B=

card of spade is picked.

P(A)=\frac{4}{52}, P(B)=\frac{13}{52}

and,

P(A \cap B)=\;\frac{1}{52}[ \because A \cap B=

Queen of spade

]

Now, required probability,

P(B/A)=\;\frac{P(A \cap B)}{P(A)}=\;\frac{\frac{1}{52}}{\frac{4}{52}}=\;\frac{1}{4}

\therefore

Option (c) is correct.

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