Question

Suppose you deal three cards, in order, from the 13 black clubs and 13 red hearts taken from an ordinary deck. How many outcomes are there for this experiment?
I got (52 choose 3)
b. ? is the probability that the first two cards dealt are red? (give as decimal).

c. What is the probability that at least one card will be red?

Answer 1

Why is it 52C3 and not 26C3 ?

Answer 2

just figured it out 26c3! thx

Answer 3

a) @terenzreignz is right, i thihnk you may have a mistake there
b) what is the probability that the first card will be red? hint, half the cards are red, half are black, that should make it simple. once you pick one red card, how many red cards are left, and whats the total amount left?
c) i don't remember how to do this one, sorry >.<

Answer 4

1/1300 is what i got for c.

Answer 5

or 7.6923 E^-4

Answer 6

I don't know what the answer to c. is [yet]
but you'll think of it this way: the total number of possibilities is the number of ways you can take three cards out of the 26.

Answer 7

@Khushal_Shah b. is 13/2600
1/1300 is what I got for c. Is it correct?

Answer 8

b should be 156/650
c is not right, the odds of picking at least 1 red card should be much greater than that, since half the cards are red

Answer 9

c. P(at least 1 red)= 1-P(no red)=1-P(all black)
Alternatively, you can use hypergeometric distribution to arrive at the same answer.

Answer 10

^ That was convenient... time to kill myself for not thinking about that :D

Answer 11

oh, true, that's one way to do it too! so your answer for c would be 1-((13/26)*(12/25)*(11/24)). Smart :)

Answer 12

@drawar how did you get B? explain please

Answer 13

compute the probability that all three cards are black
subtract that answer from one

Answer 14

how do you do that @satellite73 ?

Answer 15

can someone explain b. please? Thanks

Answer 16

@nincompoop how did you get b? explain please

Answer 17

@c2h Let's get one thing straight... probability, in general... is a fraction:
The number of "good" outcomes divided by the TOTAL number of outcomes... got it?

:D

Answer 18

how does that equal 156/650 for B)?

Answer 19

It doesn't.
On the first draw... what are the odds (what is the probability) that the first card is a red card?

Answer 20

13/52

Answer 21

.5

Answer 22

No. You only had 26 cards to start with, did you not?
0.5 (= 13/26) is correct.

Answer 23

Now, given that the first draw gave you a red card... what are the odds that the second draw gives you another red card?

Answer 24

12/25!

Answer 25

.48

Answer 26

Very good.
Now multiply them.
0.5 times 12/25.


It's not 0.48

Answer 27

not to butt in, but "odds" are not the same as probability

Answer 28

.24

Answer 29

Googled it, seems to be true. I'll remember that :)

Answer 30

thx

Answer 31

sorry to interrupt, i will be quiet now

Answer 32

Okay, @c2h 0.24 is correct, but apparently, it is equal to 156/650
Who'd have thought...
Khushal must have used combinations. It gives you ridiculously large numbers, but it all checks out in the end.

Answer 33

Are you still digesting it, @c2h ?
0.24 is correct, it is equal to 156/650

0.24 is the answer to (b)

:D

Answer 34

yes. how did Khushal get 650? I can't seem to get 156/650 on my calculator. Do you know? Thx!

Answer 35

I actually don't know how he got to 650...Curiously, why do you want to know? Wasn't the method we used more efficient, and easy? :D

Answer 36

yes thx @khush and terence

Answer 37

No problem :)