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All the jacks, queens and kings are removed from a deck of $52$ playing cards. The remaining cards are well shuffled and then one card is drawn at random. From the following choices, the probability that the card has a value $7$ is:

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752

310

15

110

answer is D.

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Detailed Solution

It is given that, all jacks, queens and kings are removed from a deck of

52

playing cards.
As the total number of cards is

52

.
In total

52

cards

4

jacks,

4

queen and

4

king cards are removed means total

12

cards are removed then the remaining cards left can be calculated as,

n (S) = 52 − 12 = 40

The card whose value is

7

could be a spade, a diamond, a club or a heart card means the number of cards whose face value is

7

would be,

n (7) = 4

Let

A

be the event, then the probability of the event can be calculated by,

P (A) = N u m b e r of favourable outcomes T o t a l number of outcomes

P (7) = n (7) n (S)

= 440 = 110

Hence, the probability is

110

.
Hence, option 4) is correct.

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