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Q.

A card is drawn at random from a pack of 52 playing cards. Find the probability that the card drawn is neither an ace nor a queen.

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a

4 13  

b

11 52  

c

3 26  

d

11 13    

answer is D.

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Detailed Solution

Given that a card is drawn at random from a pack of 52 playing cards.
We need to find the probability that the card drawn is neither an ace nor a queen.
Probability of an event E is defined as:
P(E)=Number of favorable outcomesTotal 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.
Therefore, the total number of possible outcomes is 52.
There are a total of 4 queen cards and 4 ace cards in the deck.
Therefore, the total number of favorable outcomes i.e., getting neither a jack nor a king is:
52−4−4=44  
Let E   be the event that the card drawn is neither an ace nor a queen.
Now, the probability of getting a card which is neither an ace nor a queen is:
P(E)= 44 52 ⇒P(E)= 11 13  
Thus, the probability of getting a card which is neither a jack nor a king is 11 13  .
Therefore, option 4 is correct.
 
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