GATE Civil 2015 Set 2 | GA | Question: 5

Question

Four cards are randomly selected from a pack of $52$ cards. If the first two cards are kings, what is the probability that the third card is a king?

• A. $\dfrac{4}{52} \\$
• B. $\dfrac{2}{50} \\$
• C. $\left ( \dfrac{1}{52}\right )\times\left ( \dfrac{1}{52}\right ) \\$
• D. $\left ( \dfrac{1}{52}\right )\times\left ( \dfrac{1}{51}\right )\times\left ( \dfrac{1}{50}\right )$

Comments

I think that this question is slightly ambiguous about whether the cards have been drawn all at once, or one by one.

Answer 1

There are $4$ kings in a pack of $52$ cards.
If $2$ cards are selected and both are kings, remaining cards will be $50$ out of which $2$ will be kings.

So, answer is B.