Three cards are drawn successively without replacement from a well-shuffled standard…
MATHEMATICS · Multi-part · A Level · Mathematics · Probability · Probability
Problem
Three cards are drawn successively without replacement from a well-shuffled standard deck of 52 cards. Let E1 be the event that the first card drawn is red, E2 the event that the second card drawn is an ace, and E3 the event that the third card drawn is a king. The joint probability P(E1∩E2∩E3) is known to be 22101.
(i) Express P(E1∩E2∩E3) in terms of P(E1), P(E2∣E1) and P(E3∣E1∩E2). Hence calculate the value of P(E3∣E1∩E2).
(ii) Compute the unconditional probability that the third card is a king after any two cards have been removed from the deck. Compare this probability with the value obtained in part (i) and comment on whether the events involved are independent.