question_answer

Three cards are drawn successively without replacement from a pack of 52 well-shuffled cards.  What is the probability that first two cards are king and the third card drawn is an ace?

Answer:

Since, there are 52 cards in a pack.             \[\therefore \]      \[n(S)=52\] Let A = event that the card drawn is king and B = event that the card drawn in an ace. Now,\[P(A)=\frac{4}{52}\] \[P\left( \frac{A}{A} \right)=\] Probability of drawing second king when one          king has already been drawn [ remaining cards are ]    P(B / AA) = Probability of drawing third card to be an ace when two kings have already been drawn Now, probability of getting first two cards are king and third card is an ace   [by multiplication theorem]