Question 1197137
.
Assume the random variable X has a binomial distribution with the given probability 
of obtaining a success. Find the following probability, given the number of trials 
and the probability of obtaining a success. Round your answer to four decimal places.
P(X<2), n=3, p=0.8
~~~~~~~~~~~~~~~~~


<pre>
The general formula to calculate the binomial cumulative probability (n trials; success trials from 0 to k; probability of success p) is


     P(n; i <= k; p) = {{{sum(C[n]^i*p^i*(1-p)^(n-i),i=0,k)}}},


where  {{{C[n]^i}}} = {{{n!/(i!*(n-i)!)}}} are binomial coefficients.



In your case, the number of trials is n= 3; success trials are at i= 0,1 (k=1); p = 0.8.  The formula takes the form


     P(n=3; i <= 1; p=0.8) = {{{sum(C[3]^i*p^i*(1-p)^(3-i), i=0,1)}}} = {{{C[3]*0.8^0*(1-0.8)^3}}} + {{{C[3]^1*0.8^1*(1-0.8)^(3-1)}}} = 

                          = 1*1*0.2^3 + 3*0.8*0.2^2 = use your calculator = 0.104.   <U>ANSWER</U>


<U>ANSWER</U>.  The resulting probability is P = 0.104.
</pre>

Solved.


--------------


What grade are you and which textbook do you use in your study of Probability ?