Question

Out of 5 cards, 3 are blue and 3 are red. What is the probability of drawing a blue card, replacing it, and then drawing a blue card

Answer 1

Please check your question... 3 blue and 3 red make six cards! :P

Answer 2

Unless there's a card that's both blue and red though... hmm

Answer 3

2 reds/ -.- and 3 blues.

Answer 4

OH ok :D
First, what's the probability that you draw a blue card (just once) :)

Answer 5

1/5

Answer 6

right?

Answer 7

No :)
Think of it this way
There are 5 cards, 3 of which are blue....
and 2 of which are red

It should mean that you're more likely to pick a blue card, right?

Answer 8

yeah

Answer 9

But by how much?
For instance, what are the odds of drawing a red card?

Answer 10

2/5

Answer 11

But you said the probability of getting a blue card was 1/5... something must have been wrong there ;)

Answer 12

so what are the odds of getting a blue card? :)

Answer 13

i don't know, that's why i asked you. :X lol

Answer 14

Well, you did say that the odds of getting red are 2/5... how did you get that? :)

Answer 15

so the answer is 3/5ths, right?

Answer 16

That's right :)
Now, whatever you pick the first time, it won't affect your pick for the second draw, right?

Answer 17

yepp

Answer 18

They're what you call "independent" events, and the odds of independent events happening are simply the product of their individual probabilities...
did you get that? :)

Answer 19

yes i did.

Answer 20

So, the first event's probability is
0.6
and the second event's probability is also
0.6, since you return the first card

Therefore, the probability that they both will happen is...?

Answer 21

Well, if you got
\[(\frac{3}{5})(\frac{3}{5})= \frac{9}{25} = 36\%, \]You're right!