Finding answer to probability puzzle: 5 foxes, 7 hounds run into foxhole...

[Holmes]

 

[Holmes]

Hint

View attachment 7388

Please solve this puzzle

 

[Steven G]

Please solve this puzzle

Hi, You want us to solve your puzzle? Are you kidding me? It's your puzzle so shouldn't you solve it? The volunteers are here to help with any difficulty you may have but no, we do not just do problems or puzzles for students.

 

[Holmes]

Hi, You want us to solve your puzzle? Are you kidding me? It's your puzzle so shouldn't you solve it? The volunteers are here to help with any difficulty you may have but no, we do not just do problems or puzzles for students.

I'm not a school student,I'm a grown man
I'm going through this puzzle app and got stuck

I imagined all 5 f and 7 h mixed up in an big urn
And my probability my picking a f out of the urn is 5/12
Next my probaility of picking a hound is 7/11
Again a fox is 4/10
So overall the probability is like 5/12*7/11*4/10 *5
But thats not the way to do it

But I'm now poring over the linearity of expectation math to finish this
You can download this app called probability puzzle on android
Why don't you solve it and post the steps this is classified as outrageously difficult puzzle i solved some in easy peasy and intermediate mode

 

[Steven G]

I'm not a school student,I'm a grown man
I'm going through this puzzle app and got stuck

I imagined all 5 f and 7 h mixed up in an big urn
And my probability my picking a f out of the urn is 5/12
Next my probaility of picking a hound is 7/11
Again a fox is 4/10
So overall the probability is like 5/12*7/11*4/10 *5
But thats not the way to do it

But I'm now poring over the linearity of expectation math to finish this
You can download this app called probability puzzle on android
Why don't you solve it and post the steps this is classified as outrageously difficult puzzle i solved some in easy peasy and intermediate mode

Your picture is too small to be seen-at least on my screen. So please upload a bigger picture. And by the way we are all students.

 

[Holmes]

Your picture is too small to be seen-at least on my screen. So please upload a bigger picture. And by the way we are all students.

Question is this

5foxes and 7hounds run into a hole and while inside there they got all jumbled up so all orderings are possible
Then foxes and hounds run out of the hole in a neat line,on average how many foxes are immediately followed by a hound ?

.................................
The question also gives a hint to solve that is
To make use of linearity of expectation
Find out probability of one fox followed by a hound and multiply by 5 since the probability of being immediately followed by a hound is same for all fox
..........................
FHFHFHFHFH HH

i assume FHH will not count as F is followed by 2 hounds

 

[Steven G]

Question is this

5foxes and 7hounds run into a hole and while inside there they got all jumbled up so all orderings are possible
Then foxes and hounds run out of the hole in a neat line,on average how many foxes are immediately followed by a hound ?

.................................
The question also gives a hint to solve that is
To make use of linearity of expectation
Find out probability of one fox followed by a hound and multiply by 5 since the probability of being immediately followed by a hound is same for all fox
..........................
FHFHFHFHFH HH

i assume FHH will not count as F is followed by 2 hounds

I'll work with you and assume that fhh, fhhh,... are not allowed.

Let's try to figure out how many different ways we can get fh (but not fhh...)

Let _ represent a fox.

So here are the positions of the 5 foxes: _ _ _ _ _

Suppose you want all 6 hounds together. So how many possible fh are there?

Suppose you want 5 hounds together and one alone. So how many possible fh are there?

Suppose exactly 4 hounds together and the other two together. So how many possible fh are there?

Suppose exactly 4 hounds together and the other two not together. So how many possible fh are there?

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I bet there is an easier way to do this and if there is I'm sure that pka will show us that method

 

[pka]

I imagined all 5 f and 7 h mixed up in an big urn

I can solve only if I understand. I read this as "how ways can we draw an F followed immediately by an H?"
Five F's & seven H's can be arranged in \(\displaystyle \dfrac{(5+7)!}{5!\cdot 7!}\) ways total.

Think of five blocks, \(\displaystyle \boxed{FH}\) leaving two H's.
We can arrange those seven objects in \(\displaystyle \dfrac{7!}{5!\cdot 2!}\) ways total.
That counts the number of ways we can draw an F followed immediately by an H.
Now this maybe a misreading because in includes the sting \(\displaystyle HHFHFHFHFHFH\) as well as \(\displaystyle FHHFHFHFHFHH\). Nevertheless, both of those strings have the property that each F followed immediately by an H

 

[Holmes]

Finally solved myself

The answer is 7/12*5
The probability of a hound following a fox is 7/12 which is same for all fox so 7/12*5
Wow feel good now
Thanks for your time