You have a standard deck of cards (52 cards). What is the probability you draw a four from the deck, do not replace the card, and then draw a face card (Jack, Queen,
King)?

Work Shown:

A = event of drawing a four from the deck

P(A) = 4/52, because there are 4 cards labeled "4" out of 52 total

B = event of drawing a face card on the second draw given the previous card was a "4"

P(B) = 12/51, there are 3 face cards per suit so 4*3 = 12 face cards total. There are 52-1 = 51 cards after we picked the first card and did not put it back.

P(A and B) = P(A)*P(B)

P(A and B) = (4/52)*(12/51)

P(A and B) = (4*12)/(52*51)

P(A and B) = 48/2652

P(A and B) = (4*12)/(4*221)

P(A and B) = 4/221

option (b) is correct

step-by-step explanation:

to find the solution of this system, we need to convert it into reduced row-echelon form. we have,

after applying row operations r2 -> r2/2 and r3 -> r3/3, we get,