Question 1146912
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<pre>
It is a binomial distribution type problem where the probability under the question is the sum


     P = {{{sum (C(10,k)*p^k*q^(10-k),k=4,10)}}}      (1)


The number of trials is              10;
The indexes of success trials        k = 4, 5, 6, 7, 8, 9, 10.
The probability of success trial     p = 0.35;
                                     q = 1 - p = 0.65;
C(n,k) = n! / (k! * (n-k)!)          are binomial coefficients.


The formula (1) is just a (ready to use) formal mathematical solution, and you may complete calculations manually.


But in nova days the trend is to use TECHNOLOGY for such calculations.

To use the Technology, notice that the sum  (1)  is equal to  1 - {{{sum(C(10,k)*p^k*q^(10-k),k=0,3)}}}.     (2)


Instead of calculating every term of (1) or (2) manually and then summing them up, you may use Excel function 

BINOM.DIST(3, 10, 0.35, TRUE)  to calculate the value of  {{{sum(C(10,k)*p^k*q^(10-k),k=0,3)}}}  in one click

    {{{sum(C(10,k)*p^k*q^(10-k),k=0,3)}}} = 0.513827.    


Therefore, the value of  (2)  is equal to  1 - 0.513827 = 0.486173 (approximately).    <U>ANSWER</U>
</pre>


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