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A card is drawn at random from a well shuffled pack of 52 playing cards. Find the probability of getting neither a red card nor a queen.

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\frac{7}{12}

\frac{6}{13}

\frac{7}{13}

\frac{16}{13}

answer is B.

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Detailed Solution

The total number of outcomes in a deck of playing cards is 52.
There are 26 red cards and 4 queens among which 2 are included in the red set, so we consider 2 queens in a deck of playing cards.
The

of the random experiment as,

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

The number of events getting cards neither a red card nor a queen is,
n(X) = 52 - 26 - 2

\Rightarrow n (X) = 24

So, the probability of getting cards neither a red card nor a queen is,

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

\Rightarrow P (E) = \frac{24}{52}

\Rightarrow P (E) = \frac{6}{13}

The probability of getting neither a red card nor a queen is

\frac{6}{13}

.
Hence, option 2 is the correct answer.

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