Question

Find each probability if 13 cards are drawn from a standard deck of cards
and no replacement occurs.

Answer 1

1. P(all hearts)
2. P(all red cards)
3. P(all one suit)
4. P(no kings)

Answer 2

For 1:

There are 13 cards in the deck. So how many different ways can we choose 13 cards from the set of 13 hearts? 1. And how many different ways can we choose 13 cards from the deck of 52? \(52 \choose 3\). Therefore the probability of choosing 13 hearts at random from the deck is:

\[\frac{1}{52 \choose 3} = \frac{1}{\frac{52!}{3!49!}}= \frac{1}{22100}\]

Answer 3

That's not right.

Answer 4

Should be 52 choose 13. I dunno why I have a 3 there.

Answer 5

\[\frac{1}{52 \choose 13} = \frac{1}{\frac{52!}{13!39!}}= \frac{1}{635013559600}\]

Answer 6

13 cards are drawn from =
(13/52)*(12/51)*(11/50) ..up to 13 ?

Answer 7

Yes.

Answer 8

1 and 2 the same ?

Answer 9

No, because there are twice as many red cards as there are hearts.

Answer 10

wait

Answer 11

(26/52)*(25/51)....up to 13 ?

Answer 12

13 times. Yes

Answer 13

3. P(all one suit)
(52/52)*(51/51).....up to 13
=1 ?

Answer 14

No

Answer 15

For P(all one suit) you have to realize it doesn't matter what you draw the first time, but each time after that you have to draw the same suit you picked first. So lets say you draw a heart first. What is the probability you'll draw a heart second?

Answer 16

12/51

Answer 17

And then drawing a heart the 3rd time?

Answer 18

11/50

Answer 19

And so on 12 times.

Answer 20

than start
(13/52)*(12/51)*(11/50).....up 13
the same number 1 ?

Answer 21

Which one is this for?

Answer 22

3. P(all one suit)

Answer 23

For P(all one suit) you don't care about the first card. so it's just (12/51)*(11/50)*...*(1/40)

Answer 24

4. P(no kings)
4 suite , each 13 cards , no kings
13x3= 39
stars : ( 39/52)*(38/51)......13 time

Answer 25

I disagree with the 39. From each suit there is 1 king. So there are 12 cards from each suit that are not kings. Therefore there are 12*4 = 48 cards that are not kings to choose from initially:

(48/52)*(47/51)*...*(36/40)

Answer 26

OK,TY