What are the Chances? "Recently, 4 and only 4 random people found themselves in the same room together...."

[GlenK]

Recently, 4 and only 4 random people found themselves in the same room together. I noticed that three of us were left handed and the 4th volunteered that She was left handed too. On the basis that one out of ten People are Left Handed, what is the chance that 4 left handed people find themselves in the same room?

This is not an assignment question but a curiosity question . Thank You

 

[stapel]

Recently, 4 and only 4 random people found themselves in the same room together. I noticed that three of us were left handed and the 4th volunteered that She was left handed too. On the basis that one out of ten People are Left Handed, what is the chance that 4 left handed people find themselves in the same room?

This is not an assignment question but a curiosity question . Thank You

What are your thoughts? What have you tried? Where are you stuck?

Please be complete, so we know how to start working with you. Thank you!

 

[GlenK]

If 1 out of 10 people are left handed then to have 4 in the same room, 1/(4*10) seems too
small (more Likely) where 1/(10^4) seems too large (highly unlikely) 1 in 10k, but maybe that
is the answer - I would like to know if that is right. Thank You. GlenK

 

[stapel]

If 1 out of 10 people are left handed then to have 4 in the same room, 1/(4*10) seems too
small (more Likely) where 1/(10^4) seems too large (highly unlikely) 1 in 10k, but maybe that
is the answer - I would like to know if that is right. Thank You. GlenK

By what reasoning did you arrive at these expressions? (Hint: Binomial distribution.)

 

[Harry_the_cat]

If 1 out of 10 people are left handed then to have 4 in the same room, 1/(4*10) seems too
small (more Likely) where 1/(10^4) seems too large (highly unlikely) 1 in 10k, but maybe that
is the answer - I would like to know if that is right. Thank You. GlenK

Yes 1 in 10 000 is correct. It is highly unlikely that that would happen.

 

[khansaheb]

Recently, 4 and only 4 random people found themselves in the same room together. I noticed that three of us were left handed

Note that the above event is highly unlikely too - chance of success is 1 in 1000 (= 0.1%)

 

[GlenK]

By what reasoning did you arrive at these expressions? (Hint: Binomial distribution.)

Just purely guess work using numbers available. I don't know how to prove it though. Didn't really understand the Binomial distribution - Said it required Trials. I suppose I could write a program that would randomly choose a number from 1 to 10. And if it lands on 10, 4 times in a row, then this should happen only once every 10K times.
I think I will try this so stay tuned for my results. GlenK

 

[Harry_the_cat]

It's just really a case of the multiplication theorem of probability for independent events.

In this case, Prob \(\displaystyle = \frac{1}{10} * \frac{1}{10} * \frac{1}{10} * \frac{1}{10}\).

You don't really need to know anything about the binomial distribution (although it can be done that way).

 

[GlenK]

I wrote this qbasic program and ran actual trials. You can see or try the results yourself. GlenK