PrepRung
Sign inSign up free

NDA 2019 Maths · Mathematics · Probability · medium

A card is drawn from a well-shuffled pack of 52 cards. The probability that it is a face card or a spade is

Single correct option

A card is drawn from a well-shuffled pack of 5252 cards. The probability that it is a face card or a spade is
  1. A. 2552\frac{25}{52}
  2. B. 313\frac{3}{13}
  3. C. 926\frac{9}{26}
  4. D. 1126\frac{11}{26}
Show answer and solution

Answer: (D) 1126\frac{11}{26}

There are 1212 face cards, 1313 spades, and 33 cards that are both (king, queen, jack of spades). By inclusion-exclusion the count is 12+13−3=2212+13-3=22, so the probability is 2252=1126\frac{22}{52}=\frac{11}{26}. The value 2552\frac{25}{52} double counts the three common cards.
Report a mistake

Original question written in the NDA 2019 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake