A single card is drawn at random from a well-shuffled standard deck of 52 playing cards
MATHEMATICS · Multi-part · CBSE · Mathematics · Probability · Probability
Problem
A single card is drawn at random from a well-shuffled standard deck of 52 playing cards. The card is replaced, the deck is reshuffled, and a second card is drawn.
(i) Let the event A be “drawing a King on the first draw” and the event B be “drawing a Heart on the second draw.” Find P(A), P(B) and P(A∩B).
(ii) Decide whether A and B are independent events. State your reasoning clearly.
(iii) If the first card were not replaced before the second draw, would A and B remain independent? Support your answer with appropriate calculations.