Two cards are picked from a deck. Find the probability that they are both hearts is the card are picked with replacement...the cards are picked without replacement.

Question

kropot72 · Answer

Do you know how many cards are in the suit of hearts in a standard 52 card pack?

anonymous · Answer

13.

anonymous · Answer

Would this be considered a combination and not a permutation?

kropot72 · Answer

It can be solved with basic probability theory.
Considering the first situation where the first card selected is replaced before selecting the second card, the probability of selecting hearts is 13/52 on both picks. Therefore the cards are both hearts is
$$P(both\ hearts)=\frac{13}{52}\times\frac{13}{52}=you\ can\ calculate$$
Looking at the second situation, the probability of hearts on the first pick is once again 13/52. However the conditions for the second pick are different from the first pick. This time there are 12 hearts and 51 cards in the pack. Therefore the probability of hearts is 12/51 and the probability of hearts on both picks is
$$P(both\ hearts\ without\ replacement)=\frac{13}{52}\times\frac{12}{51}=you\ can\ calculate$$

anonymous · Answer

The first one I got 1/16 and 1/17.

kropot72 · Answer

Good work! Your answers are correct.

anonymous · Answer

Than you!

kropot72 · Answer

You're welcome :)

anonymous · Answer

Oops thank you!

kropot72 · Answer

np :)