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All kings, queens and aces are removed from a pack of 52 cards. The remaining cards are well shuffled and then a card is drawn from it. Find the probability that the drawn card is a red card.

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\frac{3}{4}

\frac{1}{2}

\frac{3}{2}

\frac{1}{4}

answer is B.

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Detailed Solution

Given, total number of cards=52
There will be, Number of black cards=26
and Number of red cards=26
The P(A) of the random experiment is,

P (A) = \frac{Number of favorable outcomes}{Total number of outcomes}

Since, all kings, queens, and aces are removed from a pack of 52 cards,

\Rightarrow 4 kings + 4 queens + 4 aces = 12

So, the remaining card in a deck is,
n(S) = 52-12 = 40
Thus, the number of events getting a red card after removing all kings, queens, and aces is, n(X) = 26 - 6 = 20
So, the probability of getting a red card is,

P (E) = \frac{n (X)}{n (S)}

\Rightarrow P (E) = \frac{20}{40}

\Rightarrow P (E) = \frac{1}{2}

Therefore, the probability of getting a red card is

\frac{1}{2}

.
Hence, option 2 is the correct answer.

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