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All the three 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 black card.

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\frac{5}{49}

\frac{3}{49}

\frac{23}{49}

\frac{2}{49}

answer is C.

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Detailed Solution

Given, all the three face cards of spades are removed from a deck of 52 cards.
The P(A) of the random experiment as,

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

Since three cards of spades are lost from a pack from a deck of 52 playing cards.
So, the remaining cards in a deck are,
n(S) = 52 - 3

\Rightarrow n (S) = 49

Thus, after removing face cards, the number of black cards left,
n(X) = 13 clubs + 10 spades

\Rightarrow n (X) = 23

So, the probability of getting black cards is,

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

\Rightarrow P (E) = \frac{23}{49}

The probability of getting black cards is

\frac{23}{49}

.
Hence, option 3 is the correct answer.

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