Solution :
a). The probability that the student will
the 1st question after the 4th attempt.
P (correct in the 4th attempt)
=

= 0.01171875
b). The probability that the student will
3 questions after 10 total attempts.
P( X = 3) for X = B in (n = 10, p = 0.75)
=

= 0.0031
c). The mean and the standard deviation for the number of attempts up to when the students gets all the questions correct is :
There are = 6 success, p = 0.75.
Therefore, this is a case of a negative binomial distribution.


= 8
So,


= 1.6330