Five cards—the ten, jack, queen, king and ace of diamonds, are well-shuffled with their face downwards. One card is then picked up at random. (i) What is the probability that the card is the queen? (ii) If the queen is drawn and put aside, what is the probability that the second card picked up is (a) an ace? (b) a queen?
1/5
Explanation
This question tests understanding of probability in simple events and conditional probability when the sample space changes. In part (i), we calculate probability with all 5 cards present. In part (ii), after removing the queen, the total number of cards reduces to 4, changing the sample space. Since the queen is already drawn and put aside, there are no queens left in the remaining cards, making the probability of drawing a queen equal to 0.