Question

5 cards are drawn from a dexk of 52 cards. If all 5 are red, find the probability that they all are hearts.

Answer 1

Its a conditional probability

Answer 2

U know that?

Answer 3

yup but i am confused about the condition that all are red...

Answer 4

P(all 5 hearts / all 5 reds)

Answer 5

U need to find that.

Answer 6

but what will be their intersection..

Answer 7

P (A/B) = P ( A and B)/P(B)

Answer 8

use it.
can u?

Answer 9

but what will be P(A and B)

Answer 10

i am confused there...

Answer 11

First Find:
P(all 5 are red)

Answer 12

13C5..right

Answer 13

So, cards are not placed back.

Answer 14

And REMEMBER there are 26 red cards.

Answer 15

no....they are not placed back.....i am confuzed that sample space will be 52C5 or 26C5

Answer 16

see P(A | B) * (26C5)/(52C5) = ???

Answer 17

First, P(all 5 are red) = 26C5/52C5

Answer 18

U get that?

Answer 19

okk....that i got it right above but P(A and B) will be (13C5)/(26C5) or (13C5)/52C5

Answer 20

P( all 5 hearts and reds) = 13C5 / 52C5

Answer 21

but the answer is not matching...

Answer 22

Isnt: P(all 5 hearts / all 5 reds) = 13C5 / 26C5

Answer 23

answer is 0.11

Answer 24

i tried the same thing b4.....but nowhere near to the answer

Answer 25

pls someone help...

Answer 26

all 5 are hearts?? how is that possible?

Answer 27

There are 13 hearts....... So it is possible.

Answer 28

it is perfectly possible.....

Answer 29

oh yeah..i was thinking something else

Answer 30

He was thinking about suits. ;P

Answer 31

shouldnt it be 13C5 / 52C5 ?

Answer 32

oh no

Answer 33

you already know you have red cards so the sample space has, as @sauravshakya said, \(\binom{26}{5}\) elements in it

Answer 34

I see no mistake here: P(all 5 hearts / all 5 reds) = 13C5 / 26C5

Answer 35

yes, i was saying "on no" to the previous post

Answer 36

oh yes yes,,wont be 52C5 there..sorry..we are taking red cards only..
so i agree with saurav's ans..

Answer 37

I desperately want to say 1/6....

Answer 38

5 cards are drawn from a dexk of 52 cards. If all 5 are red, find the probability that they all are hearts.

5 cards are drawn from a dexk of 52 cards, find the probability that they all are hearts.

These are different, right?

Answer 39

I think this question is (deliberately?) confusing.

If it had said "find the CONDITIONAL probability that they all are hearts" that would have been clear.

The way it is now, there is no reason to go beyond the fact that there are 5 red cards and I would say that 1/6 is a good answer.

If the answer was written I would write the above, if a multiple choice it would depend on the choices.

I still don't know why or how the answer could be 0.11 (1/9?)

Answer 40

you get 0.11 if the problem is
3 cards are drawn (not 5)

13C3 / 26C3 =0.11

so it looks like a typo.