Drawing cards from deck

Question

From a pack of well shuffled cards, one card is drawn and kept aside. Then second card is drawn and then kept aside. After that first card (which was drawn first time) is kept back in the pack of cards, and then the third card is drawn. What is the probability that two cards are face cards

Answer 1

You are left with the 2nd card and the 3rd card.

There are a total of 52 cards and there are 12 face cards (J, Q, and K in each of the 4 suits).

The 1st draw occurs and you might draw a face card (FC) or not. So there are two possible paths. A tree diagram sometimes helps in these situations:

The two choices that result in the 2nd and third cards being face cards (FC) are shown in the diagram with red stars.

The top has a probability of (12•11•11) out of (52•51•51) = 1452/135252

The lower has a probability of (40•12•11) out of (52•51•51) = 5280/135252

So the total number successes is 1452 + 5280 = 6732 and there are 135252 total possibilities meaning the probability is 6732/135252 = 561/11271 = approximately 5%