Three cards are selected, one at a time from a standard deck of 52 cards. Let x represent the number of tens drawn in a set of three cards.
A. if this experiment is completed without replacement, explain why x is not a binomial random variable.
B. If this experiment is completed with replacement, explain why x is a binomial random variable.

Question

zarkon · Answer

if the sampling is done without replacement then the probability of 'success' changes...thus it can't be binomial

anonymous · Answer

what zarkon said

dboyette · Answer

So since the probability changes it changes the outcomes and it no longer sucess or failure?

zarkon · Answer

X is binomial if 

there are a finite # of trials
the trials are independent 
the probability of success is the same of each trial
and we let X be the number of successes

zarkon · Answer

*for each trial

anonymous · Answer

A success in this experiment is the drawing of a 10.  On the first draw the probabilty of drawing a 10 is 4 out of 52.  If you draw without replacement, there will only be 51 cards after the first draw, thus probability of success can't be the same, it will be either 4/51 (if you did not draw a 10 on the first draw) or it will be 3/51 (if you did draw a 10 on the first draw).  Either way these do not equal 4/52.  Zarkon gave the properties of the binomial experiment above.

dboyette · Answer

thank you, you explained it much better than the textbook.