Let Q denote the vent that the card drawn is a queen and K be the event that the drawn is a king. Then, we have to find `P(Q QK)`.
Probability of drawing first queen is `P(Q)=4/52`.
Now, there are 3 queens in remaining 51 cards.
Let `P(Q//Q)` be the probability of getting the second queen with the condition that one queen has already been drawn.
`:. P(Q//Q)=3/51`
Lastly, `P(K//Q Q)` is probability of third drawn card to be a king, with the condition that two queens have already been drawn.
Now, there are 4 kings in remaning 50 cards.
`:. P(K//Q Q)=4/50`.
By multiplication law of probability, we have
`P(Q QK)=P(Q nn Q nn K)`
`=P(Q).P(Q//Q).P(K//Q Q)`
`=(4/52xx3/51xx4/50)=(1/13xx1/17xx2/25)=2/5525`.
Hence, the required probability is `2/5525`.
