Question

A card is drawn from a well-shuffled pack of 52 cards. Find the probability that the card drawn is neither a jack nor a queen.

• A.
  $\frac{22}{26}$
• B.
  $\frac{45}{52}$
• C.
  $\frac{11}{13}$
• D.
  $\frac{47}{52}$

Answer 1

The correct option is C

$\frac{11}{13}$
Number of jacks in a deck of 52 cards = 4
Number of queen in a deck of 52 cards = 4
Total number of jacks and queen
= 4 + 4 = 8
Number of card which is neither a jack nor a queen = 52 - 8 = 44
$\text{Probability P(E)}$ $=\frac{\text{Number of outcomes favourable to E}}{\text{Number of all possible outcomes of the experiment}}$

$\therefore$ probability (getting ‘neither jack nor a queen’)
$=\frac{44}{52}=\frac{11}{13}$