A standard deck of 52 playing cards is well shuffled
MATHEMATICS · Multi-part · CBSE · Mathematics · Probability · Probability
Problem
A standard deck of 52 playing cards is well shuffled. Two cards are drawn successively.
(i) Without replacement, find the probability that the second card drawn is an ace, given that the first card drawn is an ace.
(ii) For the situation in part (i), calculate the probabilities of drawing an ace on the first draw and on the second draw individually, and hence decide whether the two events are independent.
(iii) Now suppose the first card is replaced and the deck is reshuffled before drawing the second card. Recalculate the conditional probability asked in part (i).
(iv) Using your calculations in parts (ii) and (iii), determine and justify whether the events “first card is an ace” and “second card is an ace” are independent when the first card is replaced.