Probability of guessing the colors of a deck of cards correctly
up vote
3
down vote
favorite
10 years ago when I was about 15 I sat down with a deck of shuffled cards and tried to guess if the next card in the deck would be red or black. In sequence I guessed 36 cards correctly as red or black, at that point my older bother came in and took told me what I was doing was stupid and I stopped being able to guess correctly. I would love to know what the probability of guessing 36 cards correctly in sequence is? Thank you
probability-theory
migrated from mathoverflow.net Dec 10 '14 at 12:39
This question came from our site for professional mathematicians.
add a comment |
up vote
3
down vote
favorite
10 years ago when I was about 15 I sat down with a deck of shuffled cards and tried to guess if the next card in the deck would be red or black. In sequence I guessed 36 cards correctly as red or black, at that point my older bother came in and took told me what I was doing was stupid and I stopped being able to guess correctly. I would love to know what the probability of guessing 36 cards correctly in sequence is? Thank you
probability-theory
migrated from mathoverflow.net Dec 10 '14 at 12:39
This question came from our site for professional mathematicians.
2
A guess of "red or black" has a high probability of being correct. You could succeed $36$ times in a row.
– Ross Millikan
Dec 10 '14 at 16:21
add a comment |
up vote
3
down vote
favorite
up vote
3
down vote
favorite
10 years ago when I was about 15 I sat down with a deck of shuffled cards and tried to guess if the next card in the deck would be red or black. In sequence I guessed 36 cards correctly as red or black, at that point my older bother came in and took told me what I was doing was stupid and I stopped being able to guess correctly. I would love to know what the probability of guessing 36 cards correctly in sequence is? Thank you
probability-theory
10 years ago when I was about 15 I sat down with a deck of shuffled cards and tried to guess if the next card in the deck would be red or black. In sequence I guessed 36 cards correctly as red or black, at that point my older bother came in and took told me what I was doing was stupid and I stopped being able to guess correctly. I would love to know what the probability of guessing 36 cards correctly in sequence is? Thank you
probability-theory
probability-theory
asked Dec 10 '14 at 10:46
Adam Sunderland
migrated from mathoverflow.net Dec 10 '14 at 12:39
This question came from our site for professional mathematicians.
migrated from mathoverflow.net Dec 10 '14 at 12:39
This question came from our site for professional mathematicians.
2
A guess of "red or black" has a high probability of being correct. You could succeed $36$ times in a row.
– Ross Millikan
Dec 10 '14 at 16:21
add a comment |
2
A guess of "red or black" has a high probability of being correct. You could succeed $36$ times in a row.
– Ross Millikan
Dec 10 '14 at 16:21
2
2
A guess of "red or black" has a high probability of being correct. You could succeed $36$ times in a row.
– Ross Millikan
Dec 10 '14 at 16:21
A guess of "red or black" has a high probability of being correct. You could succeed $36$ times in a row.
– Ross Millikan
Dec 10 '14 at 16:21
add a comment |
2 Answers
2
active
oldest
votes
up vote
1
down vote
If you just guess red or black with a 50/50 chance, without taking into account that memory of the previous cards can make a guess more accurate, then the probability of guessing 36 cards in a row correctly is:
$$left(frac 12right)^{36}$$
For comparison, if all 7.125 billion people in the world were to attempt this, the probability that anyone in the world would succeed is
$$left(frac 12right)^{36} ~~times~~ 7.125 times 10^9 = 10.4%$$
Which makes your story somewhat unbelievable.
answered Dec 10 '14 at 16:30
DanielV
17.7k42753
Well, if everybody tried this ten times in their lives, probably someone would be able to report success.
– Hagen von Eitzen
Dec 10 '14 at 16:32
add a comment |
up vote
1
down vote
If you're aiming to guess the first 36 cards right with as high a probability as possible, then the best you can do is to choose some sequence of guesses with 18 reds and 18 blacks, and all those sequences are equally likely.
Each of them has probability
$frac{(26times 25times 24timesdotstimes9)^2}{52times51times50timesdotstimes17}$
$=frac{26!times26!times16!}{52!times8!times8!}$
$approx 2.595times 10^{-11}$.
So, the chances are about 1 in 40 billion.
(Assuming the pack of cards is shuffled)
It's easier than guessing 36 coin-tosses correctly, which would have probability $2^{-36}$ which is about 1 in 70 billion.
answered Dec 10 '14 at 16:11
James Martin
20716
add a comment |
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
If you just guess red or black with a 50/50 chance, without taking into account that memory of the previous cards can make a guess more accurate, then the probability of guessing 36 cards in a row correctly is:
$$left(frac 12right)^{36}$$
For comparison, if all 7.125 billion people in the world were to attempt this, the probability that anyone in the world would succeed is
$$left(frac 12right)^{36} ~~times~~ 7.125 times 10^9 = 10.4%$$
Which makes your story somewhat unbelievable.
answered Dec 10 '14 at 16:30
DanielV
17.7k42753
Well, if everybody tried this ten times in their lives, probably someone would be able to report success.
– Hagen von Eitzen
Dec 10 '14 at 16:32
add a comment |
up vote
1
down vote
If you just guess red or black with a 50/50 chance, without taking into account that memory of the previous cards can make a guess more accurate, then the probability of guessing 36 cards in a row correctly is:
$$left(frac 12right)^{36}$$
For comparison, if all 7.125 billion people in the world were to attempt this, the probability that anyone in the world would succeed is
$$left(frac 12right)^{36} ~~times~~ 7.125 times 10^9 = 10.4%$$
Which makes your story somewhat unbelievable.
answered Dec 10 '14 at 16:30
DanielV
17.7k42753
Well, if everybody tried this ten times in their lives, probably someone would be able to report success.
– Hagen von Eitzen
Dec 10 '14 at 16:32
add a comment |
up vote
1
down vote
up vote
1
down vote
If you just guess red or black with a 50/50 chance, without taking into account that memory of the previous cards can make a guess more accurate, then the probability of guessing 36 cards in a row correctly is:
$$left(frac 12right)^{36}$$
For comparison, if all 7.125 billion people in the world were to attempt this, the probability that anyone in the world would succeed is
$$left(frac 12right)^{36} ~~times~~ 7.125 times 10^9 = 10.4%$$
Which makes your story somewhat unbelievable.
answered Dec 10 '14 at 16:30
DanielV
17.7k42753
If you just guess red or black with a 50/50 chance, without taking into account that memory of the previous cards can make a guess more accurate, then the probability of guessing 36 cards in a row correctly is:
$$left(frac 12right)^{36}$$
For comparison, if all 7.125 billion people in the world were to attempt this, the probability that anyone in the world would succeed is
$$left(frac 12right)^{36} ~~times~~ 7.125 times 10^9 = 10.4%$$
Which makes your story somewhat unbelievable.
answered Dec 10 '14 at 16:30
DanielV
17.7k42753
edited Dec 10 '14 at 16:38
answered Dec 10 '14 at 16:30
DanielV
17.7k42753
answered Dec 10 '14 at 16:30
DanielV
17.7k42753
answered Dec 10 '14 at 16:30
DanielV
17.7k42753
17.7k42753
Well, if everybody tried this ten times in their lives, probably someone would be able to report success.
– Hagen von Eitzen
Dec 10 '14 at 16:32
add a comment |
Well, if everybody tried this ten times in their lives, probably someone would be able to report success.
– Hagen von Eitzen
Dec 10 '14 at 16:32
Well, if everybody tried this ten times in their lives, probably someone would be able to report success.
– Hagen von Eitzen
Dec 10 '14 at 16:32
Well, if everybody tried this ten times in their lives, probably someone would be able to report success.
– Hagen von Eitzen
Dec 10 '14 at 16:32
add a comment |
up vote
1
down vote
If you're aiming to guess the first 36 cards right with as high a probability as possible, then the best you can do is to choose some sequence of guesses with 18 reds and 18 blacks, and all those sequences are equally likely.
Each of them has probability
$frac{(26times 25times 24timesdotstimes9)^2}{52times51times50timesdotstimes17}$
$=frac{26!times26!times16!}{52!times8!times8!}$
$approx 2.595times 10^{-11}$.
So, the chances are about 1 in 40 billion.
(Assuming the pack of cards is shuffled)
It's easier than guessing 36 coin-tosses correctly, which would have probability $2^{-36}$ which is about 1 in 70 billion.
answered Dec 10 '14 at 16:11
James Martin
20716
add a comment |
up vote
1
down vote
If you're aiming to guess the first 36 cards right with as high a probability as possible, then the best you can do is to choose some sequence of guesses with 18 reds and 18 blacks, and all those sequences are equally likely.
Each of them has probability
$frac{(26times 25times 24timesdotstimes9)^2}{52times51times50timesdotstimes17}$
$=frac{26!times26!times16!}{52!times8!times8!}$
$approx 2.595times 10^{-11}$.
So, the chances are about 1 in 40 billion.
(Assuming the pack of cards is shuffled)
It's easier than guessing 36 coin-tosses correctly, which would have probability $2^{-36}$ which is about 1 in 70 billion.
answered Dec 10 '14 at 16:11
James Martin
20716
add a comment |
up vote
1
down vote
up vote
1
down vote
If you're aiming to guess the first 36 cards right with as high a probability as possible, then the best you can do is to choose some sequence of guesses with 18 reds and 18 blacks, and all those sequences are equally likely.
Each of them has probability
$frac{(26times 25times 24timesdotstimes9)^2}{52times51times50timesdotstimes17}$
$=frac{26!times26!times16!}{52!times8!times8!}$
$approx 2.595times 10^{-11}$.
So, the chances are about 1 in 40 billion.
(Assuming the pack of cards is shuffled)
It's easier than guessing 36 coin-tosses correctly, which would have probability $2^{-36}$ which is about 1 in 70 billion.
answered Dec 10 '14 at 16:11
James Martin
20716
If you're aiming to guess the first 36 cards right with as high a probability as possible, then the best you can do is to choose some sequence of guesses with 18 reds and 18 blacks, and all those sequences are equally likely.
Each of them has probability
$frac{(26times 25times 24timesdotstimes9)^2}{52times51times50timesdotstimes17}$
$=frac{26!times26!times16!}{52!times8!times8!}$
$approx 2.595times 10^{-11}$.
So, the chances are about 1 in 40 billion.
(Assuming the pack of cards is shuffled)
It's easier than guessing 36 coin-tosses correctly, which would have probability $2^{-36}$ which is about 1 in 70 billion.
answered Dec 10 '14 at 16:11
James Martin
20716
edited Dec 11 '14 at 0:20
answered Dec 10 '14 at 16:11
James Martin
20716
answered Dec 10 '14 at 16:11
James Martin
20716
answered Dec 10 '14 at 16:11
James Martin
20716
20716
add a comment |
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f1060782%2fprobability-of-guessing-the-colors-of-a-deck-of-cards-correctly%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
2
A guess of "red or black" has a high probability of being correct. You could succeed $36$ times in a row.
– Ross Millikan
Dec 10 '14 at 16:21