
One Use of The Binomial Formula


 What's the probability exactly 3 heads are tossed if a fair coin is flipped 4 times?

 The number of trials, n, is 4.
The number of successes, x, is 3.
The probability of success, p, is .5 which makes
the probability of failure, q, .5.


 n! 
 
P(x) = 

p^{x}q^{nx} 

 (nx)! x! 
 


 4! 
 
P(3) = 

(.5)^{3}(.5)^{(43)} 

 (43)! 3! 
 


 (4)(3)(2)(1)    P(3) = 
 (.5)(.5)(.5) (.5) 
  (1) (3)(2)(1)   



 This is the same answer found in a binomial distribution table for 4 trials, using 3 successes and
a probability of .5, or 1/2, on each trial.



 The table eliminates the need for the computation and is very useful when more than one problem
or a multy step problem is considered.

 Before considering the later type of problem, note that the probability of 3 successes in 4 trials, P(x=3), when p is .8 increases to .410 and
that with p equal to .1, P(x=3) = .004.
