Question 1152814
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<pre>

This is a binomial distribution type problem, where the probability under the question is the sum


     P = {{{sum (C(7,k)*p^k*q^(7-k),k=2,7)}}}      (1)


The number of trials is              7;
The indexes of success trials        k = 2,3,4,5,6,7
The probability of success trial     p = 0.57;
                                     q = 1 - p
C(n,k) = n! / (k! * (n-k)!)          are binomial coefficients.


I am going to use the Excel standard function BINOM.DIST.

It provides calculations similar sums, but only in the case, when such sums are presented in so called <U>cumulative form</U>
as the sums from 0 to some integer number.


Therefore, I <U>convert</U> the sum (1) into the cumulative form.


In cumulative form, the sum  (1)  is equal to  1 - {{{sum(C(7,k)*p^k*q^(7-k),k=0,1)}}}.     (2)


Now, when the sum is presented in cumulative form, you may use the Excel function 

BINOM.DIST(1, 7, 0.57, TRUE)  to calculate 


    {{{sum(C(7,k)*0.57^k*(1-0.57)^(7-k),k=0,1)}}} = 0.02794.    


In this way, the value of  (2)  is equal to  1 - 0.02794 = 0.97206 (approximately).    <U>ANSWER</U>
</pre>

Thus the problem is solved using Technology.


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On Excel function BINOM.DIST, see its description everywhere, for example


https://support.office.com/en-us/article/binom-dist-function-c5ae37b6-f39c-4be2-94c2-509a1480770c



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To see other probability problems, solved by similar method, look into the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Solving-problems-on-Binomial-distribution-manually.lesson>Solving problems on Binomial distribution</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/How-to-calculate-binomial-probabilities-using-Technology.lesson>How to calculate Binomial probabilities using Technology</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Solving-problems-on-Binomial-distribution-using-Technology.lesson>Solving problems on Binomial distribution with Technology</A> 

in this site.