RAS question
One card is drawn at random from a well-shuffled pack of 52 cards. The probability that it is a king or a queen is:
Correct answer: (A) 2/13.
The probability of drawing a king or a queen from a well-shuffled 52-card pack is 2/13.
Explanation
A standard pack has 52 cards, arranged in four suits with 13 ranks in each suit; Britannica identifies queen and king as ranks in that deck. Therefore, there are four kings and four queens, giving 8 favourable cards in all. Since a single drawn card cannot be both a king and a queen, the two events are mutually exclusive. The probability is found by adding their separate probabilities: P(king or queen) = P(king) + P(queen) = 4/52 + 4/52 = 8/52. Reducing 8/52 by dividing numerator and denominator by 4 gives 2/13.
Why the other options are wrong
- (B) 1/13 counts only one four-card rank, such as kings alone or queens alone, and misses the other rank.
- (C) 4/13 would require 16 favourable cards out of 52, but kings and queens together give only 8 favourable cards.
- (D) 3/26 equals 6/52, which undercounts the favourable outcomes because there are 4 kings and 4 queens.
Concept
This tests elementary probability for mutually exclusive events: when one draw cannot satisfy both events, their probabilities are added. RAS reasoning papers frequently use card and dice examples because they check counting accuracy before formula use.