Question

A card is drawn from a deck of 52 cards. Find the probability that the card drawn is neither a black card nor a jack.

• A.
  $\frac{2}{13}$
• B.
  $\frac{4}{13}$
• C.
  $\frac{5}{13}$
• D.
  $\frac{6}{13}$

Answer 1

The correct option is D

$\frac{6}{13}$

Spades and clubs are the black cards.
Number of spades in a deck 52 cards =13
Number of clubs in a deck 52 cards = 13
Number of jacks in a deck 52 cards = 4
Total number of black card and jack = 13 + 13 + 2 = 28,(since jack of spade and jack of club are removed).
Number of cards which are neither a black card nor a jack = 52 - 28 = 24
For an event $\text{E, Probability P(E)}$ $=\frac{\text{Number of outcomes favourable to E}}{\text{Number of all possible outcomes of the experiment}}$
$\therefore$ The probability of getting neither a black card nor a jack $=\frac{24}{52}$ $=\frac{6}{13}$