Question

two cards are drawn from a pack of cards. is the expected number of hearts drawn larger when the second drawing is made with or without replacement?

Answer 1

I draw a heart for the first card.
Do I have a higher chance of getting another heart if I put that heart back in the deck or not?

Answer 2

with replacement no.. without then its the same chance

Answer 3

yes. with replacement gives you a higher number of expected hearts and a higher chance of drawing 2 hearts.

Answer 4

ok ya I got them mixed up but how do I find the expected number of hearts drawn?

Answer 5

with replacement:
13/52 x 13/52
or
1/4 x 1/4

Answer 6

without replacement
13/52 x 12/52

Answer 7

book says both answers should be 0.5

Answer 8

i'm sorry...what i gave you is the PROBABILITY of getting 2 hearts

Answer 9

lol its ok I started to get confused

Answer 10

ok. with replacement
expected number of hearts = expected number on 1st draw + expected number on 2nd draw
= 13/52 + 13/52
= 26/52 = 0.5

Answer 11

without replacement is more complicated
13/52 + 1/4(12/52) + 3/4(13/52)

Answer 12

why is it 1/4 and 3/4?

Answer 13

what do each of those number represent because im trying to get a visual

Answer 14

because the expected number of hearts on the 2nd draw depend on whether or not you got a heart on the first draw.
1/4 th of the time you will get a heart on the first draw: then 12/52 of the remaining cards are hearts
3/4ths of the time you will not get a hear on the first draw: then 13/52 of the remaining cards are hearts.

Answer 15

hmmm I guess.. thanks for your help

Answer 16

no problem