Probability Cards

Question

Two cards are drawn from a standard 52 card deck. Find the probability that a nine is drawn first and a 10 is drawn second if drawing is done with replacement.

Answer 1

there are 4 nines in a standard deck of 52 cards

so, the probability that any nine will be the top card is 4/52 = 1/13 or 1 in 13

 

if the drawn card is replaced, and the deck is shuffled, then the chance of drawing any 10 is the same, namely 1 in 13

 

if the drawn card is merely placed back on top of the deck, and it is NOT a 10, then the chance of drawing any 10 as the second card will be 4/51 = 0.078 or 7.8%