The simplified expression is ![(\frac{4}{663})](https://tex.z-dn.net/?f=%28%5Cfrac%7B4%7D%7B663%7D%29)
Step-by-step explanation:
Here, the total number of cards in a given deck = 52
let E : Event of drawing a first card which is King
Total number of kings in the given deck = 4
So,
= ![\frac{4}{52} = (\frac{1}{13} )](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B52%7D%20%20%3D%20%28%5Cfrac%7B1%7D%7B13%7D%20%29)
Now, as the picked card is NOT REPLACED,
So, now the total number of cards = 52 - 1 = 51
Total number of queen in the deck is same as before = 13
let K : Event of drawing a second card which is queen
So,
= ![(\frac{4}{51} )](https://tex.z-dn.net/?f=%28%5Cfrac%7B4%7D%7B51%7D%20%20%29)
Now, the combined probability of picking first card as king and second as queen = P(E) x P(K) = ![(\frac{1}{13}) \times(\frac{4}{51}) = (\frac{4}{663} )](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B13%7D%29%20%5Ctimes%28%5Cfrac%7B4%7D%7B51%7D%29%20%3D%20%28%5Cfrac%7B4%7D%7B663%7D%20%29)
Hence, the simplified expression is ![(\frac{4}{663})](https://tex.z-dn.net/?f=%28%5Cfrac%7B4%7D%7B663%7D%29)