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.

Explanation:

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