Question 1200778
.
A multiple-choice quiz has 15 questions, each with 4 possible answers, 
of which only 1is the correct answer. What is the probability that sheer guesswork 
yields from 5 to 10 {{{highlight(inclusive)}}} correct answers?
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<pre>
With each individual question, the probability to guess the correct answer is {{{1/4}}} = 0.25.

Next, the problem is a typical binomial distribution problem
with the number of trials n= 15, the number of success trials 5 <= k <= 10
and the individual probability of success of 0.25.


So, in this problem 

    P = P(n=15; 5 <= k <= 10; p=0.25) = P(n=15; k <= 10; p=0.25) - P(n=15; k <= 4; p=0.25).


At this point, you may use either your regular calculator TI-83/84 (function binomcdf)
or free of charge online calculator at this web-site

https://stattrek.com/online-calculator/binomial.aspx


You will get then

    P = P(n=15; 5 <= k <= 10; p=0.25) = P(n=15; k <= 10; p=0.25) - P(n=15; k <= 4; p=0.25) = 

                                      =         0.99988          - 0.68649 = 0.31339   (rounded).    <U>ANSWER</U>
</pre>

Solved.