All the face cards of spades are removed from a well shuffled pack of 52 cards. A card is then drawn at random from the remaining pack. Find the probability of getting a queen.

# All the face cards of spades are removed from a well shuffled pack of 52 cards. A card is then drawn at random from the remaining pack. Find the probability of getting a queen.

1. A

2. B

3. C

4. D

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### Solution:

Given that all the face cards of spades are removed from a well shuffled pack of 52 cards and a card is then drawn at random from the remaining pack.
We need to find the probability of getting a queen.
Probability of an event E is defined as:
$P\left(E\right)=\frac{\mathit{Number of favorable outcomes}}{\mathit{Total number of possible outcomes}}$
A deck of cards contains 52 cards in it, that are 13 spade cards, 13 heart cards, 13 diamond cards and 13 club cards.
Three face cards of spades are removed from the pack of 52 cards.
Therefore, the remaining cards in the pack are:
52 – 3 = 49
Therefore, the total number of possible outcomes is 49.
There are 4 queen cards in the whole deck, but since face cards of spades have been removed, we are left with 3 queen cards.
Therefore, the total number of favorable outcomes will be 3.
Let   be the event that a queen is drawn from the pack of 49 cards.
Now, the probability of getting a queen is,

The probability of getting a queen is  .
Therefore, option 3 is correct.

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