Jacks, queens and red kings are removed from a pack of 52 playing cards and well shuffled. A card is drawn from the remaining cards. Find the probability of getting a red card. - Sri Chaitanya Infinity Learn Best Online Courses for NCERT Solutions, CBSE, ICSE, JEE, NEET, Olympiad and Class 6 to 12

A
$712$
B
$14$
C
$1021$
D
$13$

Solution:

Given that from a pack of 52 playing cards jacks, queens and red kings are removed. One card is selected from the remaining cards.
We need to find the probability of drawing a red card.
Probability of an event E is defined as:

P (E) = \frac{Number of favorable outcomes}{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.
Jacks, queens and red kings are removed from a pack.
Therefore, the remaining cards in the pack are:

52 − 4 − 4 − 2 = 42

Therefore,the total number of possible outcomes is 42.
There are a total of 26 red cards in the whole pack but the jacks, queens and red kings are removed.
Therefore, the total number of favorable outcomes will be:

26 − 2 − 2 − 2 = 20

Let

E

be the event that a red card is drawn from the pack of 42 cards.
Now, the probability of getting a red card is,

P (E) = \frac{20}{42}

\Rightarrow P (E) = \frac{10}{21}

The probability of getting a red card is

1021

.
Therefore, option 3 is correct.

Solution:

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