A card is pulled from a well shuffled deck of standard playing cards and then put back in the deck. A second draw is made from the deck. What is the probability that an ace was drawn both times?

Question

A card is pulled from a well shuffled deck of standard playing cards and then put back in the deck.  A second draw is made from the deck.  What is the probability that an ace was drawn both times?

Damon · Answer

4/52 * 4/52

the two draws are independent because the card was put back in

IF it were not put back
THEN it would have been 4/52 * 3/51 BUT THAT IS NOT WHAT THE QUESTION IS. In other words they are trying to trick you.

Anonymous · Answer

You draw two cards from a standard deck of playing cards without replacing the first one before drawing the second.
a. Are the two outcomes on the two cards independent? Why?
b. Find P(ace on 1st card and king on 2nd)
c. You repeat this problem but this time plan to put the first card back and reshuffle the deck before selecting the second card. Are the outcomes on the two cards independent?
d. Find P(ace on 1st card and king on 2nd