Question

two card are drawn from a well shuffled deck of 51 cards. find the probability thst both cards are king( the first card is not replaced by drawing a tree diagram )​

Answer 1

Answer: P(A)=4/425≈0,0094.

Step-by-step explanation:

$P(A)=\frac{C_4^1*C_3^1}{C_{51}^2} .$

The desk has 4 kings.

First card is drawn from a well shuffled deck is a card of king.     ⇒

$C_4^1=\frac{4!}{(4-1)!*1!} =\frac{3!*4}{3!*1}=4.$

Second card is drawn from a well shuffled deck is a card of king too.    ⇒

$C_{4-1}^1=C_3^1=\frac{3!}{(3-1)!*1!}=\frac{2!*3}{2!*1}=3.\\ The \ desk\ has\ 51\ card.\ \ \ \ \Rightarrow\\C_{51}^2=\frac{51!}{(51-2)*2!}=\frac{49!*50*51}{49!*1*2} =51*25=1275.\\ P(A)=\frac{4*3}{1275} =\frac{4}{425} \approx0,0094.$