Probability and Statistics

[lucyle992]

Did I do this right?
Researchers recruited 20 volunteers - 8 men and -12 women to take part in an experiment involving a new drug and a placebo. They randomly assigned the subjects into two groups of 10 people each. To their surprise 6 of the 8 men were randomly assigned to the new drug treatment. Should they be surprised? Find the probability that a random assignment would put six men in the new drug treatment group purely by chance. Please show all of your work.

20C6 = 20P6/6! = 20*19*18*17*16*15*/6*5*4*3*2*1 = 38,760

 

[pka]

From a group of eight men and twelve women, ten are chosen at random.
The probability that six men were chosen is $\dfrac{\dbinom{8}{6}\dbinom{12}{4}}{\dbinom{20}{10}}=0.07501$
I don't know about surprises.

 

[watchkimberly]

Okay, I'm not sure how you got that? It it (8C6)*(12C4)/?

 

[Deleted member 4993]

Okay, I'm not sure how you got that? It it (8C6)*(12C4)/?

Are you not sure about the "?" (denominator) part?

It is the number of ways you can choose 10 people out of a crowd of 20 individuals.

 

[watchkimberly]

This one looks hard. I don't get it. Good luck Lucyle992.

 

[lucyle992]

I got it, thank you for your help.

 

[lucyle992]

(8P6/6!)/(12P4/4!)=13860
13860/20*19*18*17*16*15*14*13*12*11/10!=0.07501786=7.502 because I half to round.