Question

A card is drawn from a well-shuffled deck of playing cards. Find the probability of drawing a black card which is neither a face card nor an ace?

• A. $\frac{9}{52}$
• B. $\frac{9}{26}$
• C. $\frac{9}{13}$
• D. $\frac{10}{13}$

Answer 1

The correct option is B

$\frac{9}{26}$

In each suit, there are 9 cards that are not face cards and ace.
Hence, there will be a total of 18 cards in a deck which are black and are not face cards and ace.
We know that, Probability of an event E, P(E) =$\frac{\text{number of favourable outcomes}}{\text{total number of outcomes}}$
$\therefore$ Required probability is $\frac{18}{52}$ = $\frac{9}{26}$.